Giovanni Molica Bisci

Giovanni Molica Bisci
Università degli Studi di Urbino "Carlo Bo" | UNIURB · DiSPeA

About

152
Publications
18,381
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
3,604
Citations

Publications

Publications (152)
Preprint
We study the equation $-\Delta_g w+w=\lambda \alpha(\sigma) f(w)$ on a $d$-dimensional homogeneous Cartan-Hadamard Manifold $\mathcal{M}$ with $d \geq 3$. Without using the theory of topological indices, we prove the existence of infinitely many solutions for a class of nonlinearities $f$ which have an oscillating behavior either at zero or at infi...
Article
We investigate entire translating graphs constructed over the base Pn of a product space R×Pfn endowed with a weight function f which does not depend of the parameter t∈R. In this setting, assuming that the base Pn has nonnegative Bakry-Émery-Ricci tensor, we apply a f-parabolicity criterion, a suitable extension of the classical Hopf's theorem joi...
Preprint
In this paper we construct consistent examples of subgroups of $2^\omega$ with Menger remainders which fail to have other stronger combinatorial covering properties. This answers several open questions asked by Bella, Tokgoz and Zdomskyy (Arch. Math. Logic 55 (2016), 767--784).
Article
Full-text available
In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problem with critical variable exponent. By using constraint variational method and quantitative deformation lemma we show the existence of one least energy solution, which is strictly larger than twice of that of any ground state solution.
Preprint
Full-text available
We consider a smooth, complete and non-compact Riemannian manifold $(\mathcal{M},g)$ of dimension $d \geq 3$, and we look for positive solutions to the semilinear elliptic equation $$ -\Delta_g w + V w = \alpha f(w) + \lambda w \quad\hbox{in $\mathcal{M}$}. $$ The potential $V \colon \mathcal{M} \to \mathbb{R}$ is a continuous function which is coe...
Article
Full-text available
In this paper, a class of nonlocal fractional Dirichlet problems is studied. By using a variational principle due to Ricceri (whose original version was given in J. Comput. Appl. Math. 113 (2000), 401–410), the existence of infinitely many weak solutions for these problems is established by requiring that the nonlinear term f has a suitable oscilla...
Article
Full-text available
We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the Sobolev embedding sense. Our approach is of variational and topological nature. The obtained results can be viewed as a nontrivial extension to the nonlocal setting of some r...
Preprint
Full-text available
We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the sense of Sobolev embeddings. Our approach is of variational and topological nature. The obtained results can be viewed as a nontrivial extension to the nonlocal setting of so...
Book
This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an es...
Article
Full-text available
In the present paper, we show how to define suitable subgroups of the orthogonal group $${O}(d-m)$$ O ( d - m ) related to the unbounded part of a strip-like domain $$\omega \times {\mathbb {R}}^{d-m}$$ ω × R d - m with $$d\ge m+2$$ d ≥ m + 2 , in order to get “mutually disjoint” nontrivial subspaces of partially symmetric functions of $$H^1_0(\ome...
Preprint
By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main theorems, we prove the existence of at least one solution to the following singular Yamabe-type problem $$ \l...
Article
We analyse an elliptic equation with critical growth set on a d-dimensional (d≥3) Hadamard manifold (M,g). By adopting a variational perspective, we prove the existence of non-zero non-negative solutions invariant under the action of a specific family of isometries. Our result remains valid when the original nonlinearity is singularly perturbed. Pr...
Article
In this paper, we prove the existence of a sequence of nonnegative (weak) solutions for the following problem −ΔHu+u=λα(σ)f(u)inBNu∈H1,2(BN),where ΔH denotes the Laplace–Beltrami operator on the Poincaré ball model BN (with N≥3) of the hyperbolic space HN, α∈L1(BN)∩L∞(BN) is a nonnegative and not identically zero radially symmetric potential, f is...
Article
Full-text available
The purpose of this paper is to study the existence of weak solutions for some classes of one-parameter subelliptic gradient-type systems involving a Sobolev–Hardy potential defined on an unbounded domain \(\Omega _\psi \) of the Heisenberg group \({\mathbb {H}}^n={\mathbb {C}}^n\times {\mathbb {R}}\) (\(n\ge 1\)) whose geometrical profile is deter...
Article
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems{(−Δ)su+u=|u|p−2uin Ω,u≥0inΩandu≢0,u=0RN∖Ω, involving the fractional Laplacian operator (−Δ)s, where s∈(0,1), N>2s, Ω⊂RN is an exterior domain with (non-empty) smooth boundary ∂Ω and p∈(2,2s⁎). The main technical approach is based on variational...
Preprint
The purpose of this paper is to study the existence of weak solutions for some classes of one-parameter subelliptic gradient-type systems involving a Sobolev-Hardy potential defined on an unbounded domain $\Omega_\psi$ of the Heisenberg group $\mathbb{H}^n=\mathbb{C}^n\times \mathbb{R}$ ($n\geq 1$) whose geometrical profile is determined by two rea...
Article
Let m≥1 and d≥2 be integers and consider a strip-like domain O×Rd, where O⊂Rm is a bounded Euclidean domain with smooth boundary. Furthermore, let p:O¯×Rd→R be a uniformly continuous and cylindrically symmetric function. We prove that the subspace of W1,p(x,y)(O×Rd) consisting of the cylindrically symmetric functions is compactly embedded into L∞(O...
Preprint
The purpose of this paper is to study the existence of weak solutions for some classes of hemivariational problems in the Euclidean space $\mathbb{R}^d$ ($d\geq 3$). These hemivariational inequalities have a variational structure and, thanks to this, we are able to find a non-trivial weak solution for them by using variational methods and a non-smo...
Article
Full-text available
In this paper we discuss the existence and non-existence of weak solutions to parametric fractional equations involving the square root of the Laplacian A1/2 in a smooth bounded domain Ω ⊂ Rⁿ (n ≥ 2) and with zero Dirichlet boundary conditions. Namely, our simple model is the following equation {Au1 = /2 0 u = λf(u) in Ω on ∂Ω. The existence of at...
Article
Full-text available
The purpose of this paper is to study the existence of weak solutions for some classes of hemivariational problems in the Euclidean space ℝ d ( d ≥ 3). These hemivariational inequalities have a variational structure and, thanks to this, we are able to find a non-trivial weak solution for them by using variational methods and a non-smooth version of...
Article
The purpose of this paper is to study the existence of weak solutions for some classes of one-parameter subelliptic gradient-type systems involving a Sobolev–Hardy potential defined on an unbounded domain Ωψ of the Heisenberg group Hn=Cn×R ( n≥ 2) whose geometrical profile is determined by two real positive functions ψ1 and ψ2 that are bounded on b...
Article
We prove multiplicity of solutions for perturbed problems involving the square root of the Laplacian A = (-Δ)1/2. More precisely, we consider the problem where Ω ⊂ ℝ N is a bounded domain, ε ∈ ℝ, N > 1, f is a subcritical function with asymptotic linear behavior at infinity, and g is a continuous function. We also show the invariance under small pe...
Preprint
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems \begin{equation*}\label{00} \left\{ \begin{array}{l} (-\Delta)^{s}u + u = |u|^{p-2}u\;\;\mbox{in $\Omega$},\\ u \geq 0 \quad \mbox{in} \quad \Omega \quad \mbox{and} \quad u \not\equiv 0, \\ u=0 \quad \mathbb{R}^N \setminus \Omega, \end{array} \r...
Preprint
Full-text available
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems    (−∆) s u + u = |u| p−2 u in Ω, u ≥ 0 in Ω and u ≡ 0, u = 0 R N \ Ω, involving the fractional Laplacian operator (−∆) s , where s ∈ (0, 1), N > 2s, Ω ⊂ R N is an exterior domain with (non-empty) smooth boundary ∂Ω and p ∈ (2, 2 * s). The ma...
Article
In this paper we study the existence of (weak) solutions for some Kirchhoff-type problems whose simple prototype is given by [Formula presented]where ΔH denotes the Laplace–Beltrami operator on the ball model of the Hyperbolic space [Formula presented] (with N≥3), a,b and λ are real parameters, [Formula presented] is a geodesic ball centered in zer...
Article
In this paper, we deal with the following fractional nonlocal p-Laplacian problem: u u (− ≥ = ∆) 0 0sp u u = ≢ λβ 0 (x)uq + f(u) in Ω, in Ω, in RN \ Ω, where Ω ⊂ RN is a bounded domain with a smooth boundary of RN, s ∈ (0, 1), p ∈ (1, ∞), N > sp, λ is a real parameter, β ∈ L∞(Ω) is allowed to be indefinite in sign, q > 0 and f : [0, +∞) → R is a co...
Article
Full-text available
In this paper, we discuss the existence and multiplicity of periodic solutions for a class of parametric nonlocal equations with critical and supercritical growth. It is well known that these equations can be realized as local degenerate elliptic problems in a half-cylinder of \(\mathbb {R}^{N+1}_{+}\) together with a nonlinear Neumann boundary con...
Article
The purpose of this paper is to study the existence of weak solutions for some classes of Schrödinger equations defined on the Euclidean space {\mathbb{R}^{d}} ( {d\geq 3} ). These equations have a variational structure and, thanks to this, we are able to find a non-trivial weak solution for them by using the Palais principle of symmetric criticali...
Article
Full-text available
In this paper we are concerned with the multiplicity of solutions for the following fractional Laplace problem $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u= \mu |u|^{q-2}u + |u|^{2^*_s-2}u &{}\quad \text{ in } \Omega \\ u=0 &{}\quad \text{ in } {\mathbb {R}}^n{\setminus } \Omega , \end{array}\right. \end{aligned}$$where \(\Omega \sub...
Article
In this paper, we use the Limit Index Theory due to Li 19 and the fractional version of concentration compactness principle to study the multiplicity of solutions for a class of noncooperative fractional p‐Laplacian elliptic system with homogeneous Dirichlet boundary conditions involving the critical exponents.
Article
Full-text available
In this paper we discuss the existence and non--existence of weak solutions to parametric equations involving the Laplace-Beltrami operator $\Delta_g$ in a complete non-compact $d$--dimensional ($d\geq 3$) Riemannian manifold $(\mathcal{M},g)$ with asymptotically non--negative Ricci curvature and intrinsic metric $d_g$. Namely, our simple model is...
Article
Full-text available
This paper deals with multiplicity and bifurcation results for nonlinear problems driven by the fractional Laplace operator $(-\Delta)^s$ and involving a critical Sobolev term. In particular, we consider $$\begin{cases} (-\Delta)^su=\gamma|u|^{2^*-2}u+f(x,u) & \mbox{in } \Omega u=0 & \mbox{in } \mathbb R^n\setminus \Omega, \end{cases}$$ where $\Ome...
Article
The paper deals with the existence of at least one (weak) solution for a wide class of one-parameter subelliptic critical problems in unbounded domains Ω of a Carnot group G, which present several difficulties, due to the intrinsic lack of compactness. More precisely, when the real parameter is sufficiently small, thanks to the celebrated symmetric...
Article
This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi–nonlocal operator u ↦ M(∥u∥²)(−Δ)su, where M models a Kirchhoff–type coefficient while (−Δ)s denotes the fractional Laplace operator. More precisely, by adapting to our bi–nonlocal framework the variational and topological tool...
Article
By using variational methods, in this paper we study a nonlinear elliptic problem defined in a bounded domain Ω ⊂ ℝN, with smooth boundary ∂Ω, involving fractional powers of the Laplacian operator together with a suitable nonlinear term f. More precisely, we prove a characterization theorem on the existence of one weak solution for the elliptic pro...
Article
This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the treated problem is obtained exploiting a local minimum theorem for differentiable functionals defined on refl...
Article
Full-text available
This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity. As a special case of our results we prove the existence of at least one nontrivial solution for a subelliptic critical equation defined on a smooth and bounded domain $D$ of the {Heisenberg gr...
Article
Full-text available
This article concerns a class of elliptic equations on Carnot groups depending on one real positive parameter and involving a subcritical nonlinearity (for the critical case we refer to G. Molica Bisci and D. Repov\v{s}, Yamabe-type equations on Carnot groups, Potential Anal. 46:2 (2017), 369-383; arXiv:1705.10100 [math.AP]). As a special case of o...
Article
Full-text available
In this paper, we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian (Formula presented.) in a smooth bounded domain (Formula presented.) ((Formula presented.)) and with Dirichlet zero-boundary conditions, i.e.(Formula presented.) The existence of at least three (Formula present...
Article
Full-text available
The aim of this paper is to deal with the nonlocal fractional counterpart of the Laplace equation involving critical nonlinearities studied by Brezis and Nirenberg. Namely, our model is the equation (-Δ)s pu = |u|p ∗ s -2u + λg(x, u) inΩ u = 0 in Rn \ Ω, where (-Δ)s p is the fractional p-Laplace operator, s ∈ (0, 1), Ω is an open bounded set of Rn,...
Article
Full-text available
We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index theory developed by Bartolo, Benci and Fortunato \cite{bbf} after transforming the problem to a degenerate elli...
Article
Full-text available
We study the question of the existence of infinitely many weak solutions for nonlocal equations of fractional Laplacian type with homogeneous Dirichlet boundary data, in presence of a superlinear term. Starting from the well-known Ambrosetti–Rabinowitz condition, we consider different growth assumptions on the nonlinearity, all of superlinear type....
Article
Full-text available
We consider the following class of fractional Schrödinger equations: (-\Delta)^{\alpha}u+V(x)u=K(x)f(u)\quad\text{in }\mathbb{R}^{N}, where {\alpha\in(0,1)} , {N>2\alpha} , {(-\Delta)^{\alpha}} is the fractional Laplacian, V and K are positive continuous functions which vanish at infinity, and f is a continuous function. By using a minimization arg...
Article
Full-text available
By using variational methods, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established in presence of a perturbed Lipschitz term. Our goal was achieved requiring an appropriate behavior of the nonlinear term $f$, either at zero or at infinity, without symmetry conditions.
Article
Full-text available
The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result coming out from a classical Pucci-Serrin theorem in addition to a local minimum result for differentiable function...
Article
We are concerned with existence results for a critical problem of Brézis-Nirenberg-type driven by an integro-differential operator of fractional nature. The latter includes, for a specific choice of the kernel, the usual fractional Laplacian. Under mild assumptions on the subcritical part of the nonlinearity, we provide first the existence of one w...
Article
In this paper we study the multiplicity of weak solutions to (possibly resonant) nonlocal equations involving the fractional p-Laplacian operator. More precisely, we consider a Dirichlet problem driven by the fractional p-Laplacian operator and involving a subcritical nonlinear term which does not satisfy the technical Ambrosetti–Rabinowitz conditi...
Book
This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes a...
Article
Full-text available
The aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach co...
Article
In this paper, we apply Morse theory and local linking to study the existence of nontrivial solutions for Kirchhoff type equations involving the nonlocal fractional $p$-Laplacian with homogeneous Dirichlet boundary conditions: \begin{align*} \begin{cases} \!\bigg[M\bigg(\displaystyle\iint_{\mathbb{R}^{2N}}\!\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\bi...
Article
Full-text available
The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.
Article
Full-text available
The aim of this paper is to establish the multiplicity of weak solutions for a Kirchhoff-type problem driven by a fractional p-Laplacian operator with homogeneous Dirichlet boundary conditions: where is an open bounded subset of with Lipshcitz boundary , is the fractional p-Laplacian operator with 0 < s < 1 < p < N such that sp < N, M is a continu...
Article
Full-text available
The aim of this paper is to prove multiplicity of solutions for nonlocal fractional equations modeled by $$ \left\{ \begin{array}{ll} (-\Delta)^s u-\lambda u=f(x,u) & {\mbox{ in }} \Omega\\ u=0 & {\mbox{ in }} \mathbb{R}^n\setminus \Omega\,, \end{array} \right. $$ where $s\in (0,1)$ is fixed, $(-\Delta)^s$ is the fractional Laplace operator, $\lamb...
Article
In this paper, we study a highly nonlocal parametric problem involving a fractional-type operator combined with a Kirchhoff-type coefficient. The latter is allowed to vanish at the origin (degenerate case). Our approach is of variational nature; by working in suitable fractional Sobolev spaces which encode Dirichlet homogeneous boundary conditions,...
Article
Full-text available
In this work we investigate multiple solutions to discrete inclusions with the -Laplacian problem. We focus on the existence of three solutions with the aid of linking arguments and a new non-smooth three critical points tool, which we provide.
Article
Full-text available
In this paper we consider the following critical nonlocal problem {-L(K)u =lambda u + vertical bar u vertical bar(2*-2)u in Omega u=0 in R-n\Omega where s is an element of (0, 1), Omega is an open bounded subset of R-n n > 2s, with continuous boundary, lambda is a positive real parameter, 2* = 2n/(n - 2s) is the fractional critical Sobolev exponent...
Article
We establish a Caccioppoli-type inequality for a second-order degenerate elliptic systems of -Laplacian type. As a direct consequence, exploiting classical Campanato’s approach and the hole-filling technique due to Widman, we are able to prove a global regularity result on Morrey’s and spaces, with .
Article
In this paper we study a highly nonlocal problem involving a fractional operator combined with a Kirchhoff-type coefficient. The latter is allowed to vanish at the origin (degenerate case). Precisely, we consider the following nonlocal problem (Equation Presented) where r ≥ 0, s ∈ (0, 1), ω b is an open bounded subset of Rn, n > 2s, with continuous...
Article
Full-text available
Some existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution.
Article
This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for d...
Article
Full-text available
In this paper, by using variational methods, we study the following elliptic problem involving a general operator in divergence form of p-Laplacian type (p > 1). In our context, Ω is a bounded domain of ℝN, N ≥ 3, with smooth boundary ∂Ω, A is a continuous function with potential a, λ is a real parameter, β ∈ L∞(Ω) is allowed to be indefinite in si...
Article
Full-text available
In this paper we prove a characterization theorem on the existence of one non-zero strong solution for elliptic equations defined on the Sierpinski gasket. More generally, the validity of our result can be checked studying elliptic equations defined on self-similar fractal domains whose spectral dimension nu is an element of (0, 2). Our theorem can...
Article
Full-text available
In this paper we study the existence of infinitely many weak solutions for equations driven by nonlocal integrodifferential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian where s ∈ (0, 1) is fixed. We consider different superlinear growth assumptions on the nonlinearity, st...
Article
In the present paper, we study the weak lower semicontinuity of the functional Phi(lambda,gamma)(u) : = 1/2 integral R-n x R-n vertical bar u(x) - x(y)vertical bar(2)/vertical bar x - y vertical bar(n+2s) dx dy - lambda/2 lambda/2 f(Omega) vertical bar u(x)vertical bar(2)dx -gamma/2 (integral(Omega)vertical bar u(x)vertical bar(2)* dx)(2/2*) where...
Article
Full-text available
In this paper, we study the existence of multiple ground state solutions for a class of parametric fractional Schrödinger equations whose simplest prototype is (Formula Presented.),where n>2, (-Δ)s stands for the fractional Laplace operator of order s∈(0,1), and λ is a positive real parameter. The nonlinear term f is assumed to have a superlinear b...
Article
In this work we obtain an existence result for a class of singular quasilinear elliptic Dirichlet problems on a smooth bounded domain containing the origin. By using a Caffarelli-Kohn-Nirenberg type inequality, a critical point result for differentiable functionals is exploited, in order to prove the existence of a precise open interval of positive...
Article
Full-text available
In this paper, using a Hodge-type decomposition of variable exponent Lebesgue spaces of Clifford-valued functions and variational methods, we study the properties of weak solutions to the homogeneous and nonhomogeneous A-Dirac equations with variable growth in the setting of variable exponent Sobolev spaces of Clifford-valued functions.
Article
Full-text available
We study a nonlocal Neumann problem driven by a nonhomogeneous elliptic differential operator. The reaction term is a nonlinearity function that exhibits p-superlinear growth but need not satisfy the Ambrosetti–Rabinowitz condition. By using an abstract linking theorem for smooth functionals, we prove a multiplicity result on the existence of weak...
Article
Full-text available
This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. I...
Article
The aim of this paper is investigating the existence and multiplicity of weak solutions to non-local equations involving a general integro-differential operator of fractional type, when the nonlinearity is subcritical and asymptotically linear at infinity. More precisely, in presence of an odd symmetric non-linear term, we prove multiplicity result...
Article
Full-text available
The aim of this paper is to study a class of nonlocal fractional Laplacian equations depending on two real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci, we establish the existence of three weak solutions for nonlocal fractional problems exploiting an abstract criti...
Article
In the present paper, by using variational methods, we study the existence of multiple nontrivial weak solutions for parametric nonlocal equations, driven by the fractional Laplace operator (-Δ)s, in which the nonlinear term has a sublinear growth at infinity. More precisely, a critical point result for differentiable functionals is exploited, in o...
Article
In this paper we are interested in the existence of infinitely many solutions for a partial discrete Dirichlet problem depending on a real parameter. More precisely, we determine unbounded intervals of parameters such that the treated problems admit either an unbounded sequence of solutions, provided that the nonlinearity has a suitable behaviour a...
Article
In this paper we consider problems modeled by the following nonlocal fractional equation {(-Δ)su+a(x)u=μf(u)in Ωu=0in Rn\Ω, where s∈(0,1) is fixed, Ω is an open bounded subset of Rn, n>2s, with Lipschitz boundary, (-Δ)s is the fractional Laplace operator and μ is a real parameter. Under two different types of conditions on the functions a and f, by...
Article
Full-text available
We discuss multiplicity of non-negative solutions of a parametric one-dimensional mean curvature problem. Our main effort here is to describe the configuration of the limits of a certain function depending on the potential F at zero that yield, for \lambda belonging to a suitable real interval, the existence of infinitely many weak non-negative and...
Article
Full-text available
In this paper the existence of infinitely many solutions for a class of Kirchhoff-type problems involving the p-Laplacian, with p>1, is established. By using variational methods, we determine unbounded real intervals of parameters such that the problems treated admit either an unbounded sequence of weak solutions, provided that the nonlinearity has...
Article
Full-text available
In this paper, we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. Non-trivial solutions are obtained by computing the critical groups and Morse theory. Our results extend some classical theorems for semilinear elliptic equations to the non-...
Article
Full-text available
This work is devoted to the study of the existence of at least one (non-zero) solution to a problem involving the discrete p-Laplacian. As a special case, we derive an existence theorem for a second-order discrete problem, depending on a positive real parameter a, whose prototype is given by [GRAPHICS] , Our approach is based on variational methods...
Article
This article concerns a class of nonlocal fractional Laplacian problems depending of three real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci (in order to correctly encode the Dirichlet boundary datum in the variational formulation of our problem) we establish the e...
Article
Full-text available
This work is devoted to study the existence of solutions to nonlocal equations involving the p-Laplacian. More precisely, we prove the existence of at least one nontrivial weak solution, and under additional assumptions, the existence of infinitely many weak solutions. In order to apply mountain pass results, we require rather general assumptions o...
Article
In this work we obtain existence results for some singular elliptic Dirichlet problems involving the p–Laplacian. Precisely, starting from a weak lower semicontinuity result and by using the classical Hardy inequality, a critical point result for differentiable functionals is exploited, in order to prove the existence of a precise open interval of...
Article
In this note a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one-dimensional fractional problems admits at least one non-trivial solution under an asymptotical behaviour of the nonlinear datum at zero. A concrete example of an application is then presented.
Article
Dans cette Note, nous étudions lʼexistence de solutions à basse ou à haute énergie pour une classe de problèmes elliptiques contenant un terme non linéaire oscillatoire autour de lʼorigine ou à lʼinfini. Nous mettons en évidence lʼeffet de compétition entre la non-linéarité oscillatoire, le terme à croissance polynomiale et les valeurs dʼun paramèt...
Article
Full-text available
In this article, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the p-biharmonic operator is investigated. Moreover, a concrete example of an application is presented.
Article
Full-text available
In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special cases are analyzed. In conclusion, for completeness, a concrete example of an application is presented by findin...
Article
Full-text available
The objective of this paper is to design the radio resource management (RRM) policies for support-ing the effective delivery of multicast service in LTE-A (Long Term Evolution -Advanced) systems. Specifically, we propose multicast subgrouping based solutions to maximize the system efficiency in terms of throughput under the constraints that: (i) al...
Article
Full-text available
In this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.
Article
Full-text available
This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the fractional Laplacian, finding a nontrivial weak solution of the equation (-Δ)su=h(x)f(u) in Ω, u=0 in Rn, where h∈L∞+()...
Article
Full-text available
We study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator div(a(x, ∇u)), a special case of which is the p-Laplacian. The reaction term is a nonlinearity function f which exhibits (p-1)-subcritical growth. By using variational methods, we prove a multiplicity result on the existence of weak...

Network

Cited By