Jleli Mohamed

• King Saud University

The goal of this paper is to study the nonexistence of local weak solutions to a generalized drift wave differential inequality of Sobolev type posed in infinite parallelepiped, under an inhomogeneous Dirichlet boundary condition. Our approach is based on the construction of suitable test functions.

We introduce two new classes of single-valued contractions of polynomial type defined on a metric space. For the first one, called the class of polynomial contractions, we establish two fixed point theorems. Namely, we first consider the case when the mapping is continuous. Next we weaken the continuity condition. In particular, we recover Banach’s...

In this paper, we are concerned with the study of the existence of fixed points for single and multivalued three-points contractions. Namely, we first introduce a new class of single-valued mappings defined on a metric space equipped with three metrics. A fixed point theorem is established for such mappings. The obtained result recovers that establ...

In this paper, we are concerned with the study of the existence of fixed points for single and multi-valued three-points contractions. Namely, we first introduce a new class of single-valued mappings defined on a metric space equipped with three metrics. A fixed point theorem is established for such mappings. The obtained result recovers that estab...

Let \(R\subset \mathbb {R}^N\backslash \{0\}\) be a root system and \(R^+\) be a positive subsystem. Let k be a nonnegative multiplicity function defined on R and invariant by the the reflection group and \(\gamma =\sum _{\alpha \in R^+}k(\alpha )\). This paper is devoted to study the semilinear inequality where \(\Delta _k\) is the Dunkl Laplacian...

In this study, we introduce the notion of α \alpha -convex sequences which is a generalization of the convexity concept. For this class of sequences, we establish a discrete version of Fejér inequality without imposing any symmetry condition. In our proof, we use a new approach based on the choice of an appropriate sequence, which is the unique sol...

Let Δ k {\Delta }_{k} be the Dunkl generalized Laplacian operator associated with a root system R R of R N {{\mathbb{R}}}^{N} , N ≥ 2 N\ge 2 , and a nonnegative multiplicity function k k defined on R R and invariant by the finite reflection group W W . In this study, we study the existence and nonexistence of weak solutions to the semilinear inequa...

Fejér’s integral inequality is a weighted version of the Hermite-Hadamard inequality that holds for the class of convex functions. To derive his inequality, Fejér [Über die Fourierreihen, II, Math. Naturwiss, Anz. Ungar. Akad. Wiss. 24 (1906), 369–390] assumed that the weight function is symmetric w.r.t. the midpoint of the interval. In this study,...

Retinopathy is a group of retinal disabilities that causes severe visual impairments or complete blindness. Due to the capability of optical coherence tomography to reveal early retinal abnormalities, many researchers have utilized it to develop autonomous retinal screening systems. However, to the best of our knowledge, most of these systems rely...

A system of time‐fractional diffusion equations posed in an exterior domain of ℝN$$ {\mathrm{\mathbb{R}}}^N $$( N≥3$$ N\ge 3 $$) under homogeneous Dirichlet boundary conditions is investigated in this paper. The time‐fractional derivatives are considered in the Caputo sense. Using nonlinear capacity estimates specifically adapted to the nonlocal pr...

For a given sequence a = ( a 1 , … , a n ) ∈ R n a=\left({a}_{1},\ldots ,{a}_{n})\in {{\mathbb{R}}}^{n} , our aim is to obtain an estimate of E n ≔ a 1 + a n 2 − 1 n ∑ i = 1 n a i {E}_{n}:= \left|\hspace{-0.33em},\frac{{a}_{1}+{a}_{n}}{2}-\frac{1}{n}{\sum }_{i=1}^{n}{a}_{i},\hspace{-0.33em}\right| . Several classes of sequences are studied. For eac...

A nonlinear time-fractionally damped wave equation with an inverse-square potential posed on the interval (0, 1) is investigated. The time-fractionally derivative is considered in the Caputo sense. A weight function of the form x −σ ( σ∈R ) is allowed in front of the nonlinearity ∣u(t, x)∣ p (p > 1). The problem is studied under certain initial con...

We introduce two new classes of single-valued contractions of polynomial type defined on a metric space. For the first one, called the class of polynomial contractions, we establish two fixed point theorems. Namely, we first consider the case when the mapping is continuous. Next, we weaken the continuity condition. In particular, we recover Banach'...

We consider weak solutions of the nonlinear time-fractional biharmonic diffusion equation $\partial _{t}^{\alpha }u+\partial _{t}^{\beta }u+u_{xxxx}=h(t,x)|u|^{p}$ ∂ t α u + ∂ t β u + u x x x x = h ( t , x ) | u | p in $(0,\infty )\times (0,1)$ ( 0 , ∞ ) × ( 0 , 1 ) subject to the initial conditions $u(0,x)=u_{0}(x)$ u ( 0 , x ) = u 0 ( x ) , $u_{t...

In this paper, we deal with models with Born-Infeld (or relativistic ) type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first provide an estimate of the critical speed and then, through a careful analysis of an equiv...

We establish weighted Hermite-Hadamard-type inequalities for some classes of differentiable functions without assuming any symmetry property on the weight function. Next, we apply our obtained results to the approximation of some classes of weighted integrals.

In recent times, the quality of life of several individuals has been affected by chronic diseases. Traditional forms of rehabilitation occasionally involve face-to-face sessions, which restricts accessibility and presents challenges for real-time monitoring. Lack of comprehensive understanding of the aspects impacts long-term patient engagement and...

A nonlinear time-fractional cable equation posed on the interval $ (0, 1) $ under a homogeneous Dirichlet boundary condition is investigated in this work. The considered equation reflects the anomalous electro-diffusion in nerve cells. Using nonlinear capacity estimates specifically adapted to the considered problem, we establish sufficient conditi...

In this paper, we first introduced the notion of $ \theta $-hyperbolic sine distance functions on a metric space and studied their properties. We investigated the existence and uniqueness of fixed points for some classes of single-valued mappings defined on a complete metric space and satisfying contractions involving the $ \theta $-hyperbolic sine...

We consider a wave inequality in an exterior domain of RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^{N}$$\end{document}, involving the product of two...

Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal of this paper is to study the nonexistence of weak solutions to a time-fracti...

We establish necessary conditions for the existence of solutions to various systems of partial differential inequalities in the plane. The obtained conditions provide new Hermite-Hadamard-type inequalities for differentiable functions in the plane. In particular, we obtain a refinement of an inequality due to Dragomir [On the Hadamard’s inequality...

We consider hyperbolic inequalities with Hardy potential u t t − Δ u + λ | x | 2 u ⩾ | x | − a | u | p in ( 0 , ∞ ) × B 1 ∖ { 0 } , u ( t , x ) ⩾ f ( x ) on ( 0 , ∞ ) × ∂ B 1 , where B 1 is the unit ball in R N , N ⩾ 3, λ > − ( N − 2 2 ) 2 , a ⩾ 0, p > 1 and f is a nontrivial L 1 -function. We study separately the cases: λ = 0, − ( N − 2 2 ) 2 < λ...

We investigate the existence and nonexistence of weak solutions to a (3+1)-dimensional equation of plasma drift waves perturbed by a singular potential. The considered equation is posed in an infinite parallelepiped, under an inhomogeneous Dirichlet boundary condition. We show that the dividing line with respect to existence or nonexistence is give...

A Schrödinger equation with a time-fractional derivative, posed in (0,∞)×I, where I=]a,b], is investigated in this paper. The equation involves a singular Hardy potential of the form λ(x−a)2, where the parameter λ belongs to a certain range, and a nonlinearity of the form μ(x−a)−ρ|u|p, where ρ≥0. Using some a priori estimates, necessary conditions...

We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using nonlinear capacity estimates, we establish suffic...

We consider a class of nonlinear higher-order evolution inequalities posed in $(0,\infty)\times B_1\backslash\{0\}$, subject to inhomogeneous Dirichlet-type boundary conditions, where B1 is the unit ball in $\mathbb{R}^N$. The considered class involves differential operators of the form \begin{equation*} \mathcal{L}_{\mu_1,\mu_2}=-\Delta +\frac{\mu...

We study the existence and nonexistence of solutions to a system of wave inequalities with inverse-square potentials in an exterior domain of RN, under inhomogeneous Dirichlet-type boundary conditions. Our study yields naturally existence and nonexistence results for the corresponding stationary wave system.

Hermite–Hadamard inequality is a double inequality that provides an upper and lower bounds of the mean (integral) of a convex function over a certain interval. Moreover, the convexity of a function can be characterized by each of the two sides of this inequality. On the other hand, it is well known that a twice differentiable function is convex, if...

Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x

Functional inequalities involving special functions are very useful in mathematical analysis, and several interesting results have been obtained in this topic. Several methods have been used by many authors in order to derive upper or lower bounds of certain special functions. In this paper, we establish some general integral inequalities involving...

We are concerned with the study of existence and nonexistence of weak solutions for a class of hyperbolic inequalities with a Hardy potential singular on the boundary $ \partial B_1 $ of the annulus $ A = \left\{x\in \mathbb{R}^3: 1 < |x|\leq 2\right\} $, where $ \partial B_1 = \left\{x\in \mathbb{R}^3: |x| = 1\right\} $. A singular potential funct...

We investigate the existence and nonexistence of nonnegative radial solutions to exterior problems of the form Δ H m u ( q ) + λ ψ ( q ) K ( r ( q ) ) f ( r 2 − Q ( q ) , u ( q ) ) = 0 {\Delta }_{{{\mathbb{H}}}^{m}}u\left(q)+\lambda \psi \left(q)K\left(r\left(q))f\left({r}^{2-Q}\left(q),u\left(q))=0 in B 1 c {B}_{1}^{c} , under the Dirichlet bounda...

In this paper, a new class of generalized distance functions with respect to a pair of mappings is introduced. Next, some inequalities involving such distance functions are established. Our obtained results generalize and cover some recent results from the literature. Moreover, new distance inequalities for self-crossing polygons are obtained.

We consider a class of hyperbolic inequalities with nonlinear convolution terms on complete noncompact Riemannian manifolds. We establish sufficient conditions depending on the geometry of the manifold and the parameters of the problem, for which there is no nontrivial global weak solution. Moreover, in the Euclidean case, the existence of positive...

We study the existence and nonexistence of weak solutions to a semilinear higher order (in time) evolution inequality involving a convection term in the exterior of the half-ball, under Dirichlet-type boundary conditions. A weight function of the form $ |x|^a $ is allowed in front of the power nonlinearity. When $ a > -2 $, we show that the dividin...

In this paper, a system of nonlinear delay integral equations related to the spread of certain infectious diseases is investigated. Namely, using Perov’s fixed-point theorem, we obtain sufficient conditions for which the system admits a unique positive solution, and provide a numerical algorithm that converges to this solution. Moreover, we establi...

We establish new blow-up results for a higher order (in time) evolution inequality involving a convection term in an exterior domain of RN. We study two types of inhomogeneous boundary conditions: Dirichlet and Neumann. Using a unified approach, we obtain optimal criteria of Fujita type for each case. Our study yields naturally optimal nonexistence...

We investigate the large time behavior of solutions to a class of inhomogeneous hyperbolic inequalities involving combined nonlinearities of the form |u|p+1Γ(σ)∫0t(t−s)σ−1|∇u(s,x)|qds+w(x), where p,q>1 and σ>0. We show that, if w has a positive average, then the considered class admits no global weak solution. Our approach is based on nonlinear cap...

This paper is concerned with nonexistence results for a class of nonlinear hyperbolic inequalities with a potential function V=V(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{...

We study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation $$\begin{aligned} iu_t+\Delta u=\lambda |u|^p+\mu |\nabla u|^q+w(x),\quad t>0,\, x\in {\mathbb {R}}^N, \end{aligned}$$ i u t + Δ u = λ | u | p + μ | ∇ u | q + w ( x ) , t > 0 , x ∈ R N , where $$N\ge 1$$ N ≥ 1 , $$p,q>1$$ p , q > 1 , $$\lambda ,\mu \i...

We consider the nonlinear hyperbolic‐type inequality ∂ttu−Δu≥|u|p+|∇u|q+w(x),(t,x)∈(0,∞)×ℝ+N$$ {\partial}_{tt}u-\Delta u\ge {\left|u\right|}^p+{\left|\nabla u\right|}^q+w(x),\left(t,x\right)\in \left(0,\infty \right)\times {\mathbb{R}}_{+}^N $$ under the Dirichlet‐type boundary condition u(t,x′,0)≥0,(t,x′)∈(0,∞)×ℝN−1,$$ u\left(t,{x}^{\prime },0\rig...

We are concerned with nonexistence results for a class of systems of parabolic inequalities in (0,∞)×A, where A={x∈RN:1<|x|≤2}. The considered systems involve a singular potential function V(x)=(|x|−1)−ρ, ρ>0, in front of the power nonlinearities. Two types of inhomogeneous boundary conditions on ∂B2={x∈RN:|x|=2} are discussed: Neumann type conditi...

We establish sufficient conditions for the nonexistence of nontrivial solutions to higher order evolution inequalities, with respect to the time variable. We consider a nonlocal source term, and work on complete noncompact Riemannian manifolds. The obtained conditions depend on the parameters of the problem and the geometry of the manifold. Our mai...

We are concerned with the existence and nonexistence of global weak solutions for a certain class of time-fractional inhomogeneous pseudo-parabolic-type equations involving a nonlinearity of the form |u|p+ι|∇u|q, where p,q>1, and ι≥0 is a constant. The cases ι=0 and ι>0 are discussed separately. For each case, the critical exponent in the Fujita se...

We consider a fractional differential inequality involving $ \psi $-Caputo fractional derivatives of different orders, with a polynomial nonlinearity and a singular potential term. Using the test function method and some integral inequalities, we establish nonexistence criteria of global solutions in both cases: $ \lim\limits_{t\to \infty}\psi(t)=\...

We are concerned with the nonexistence of sign-changing global weak solutions for a class of semilinear parabolic differential inequalities with convection terms in exterior domains. A weight function of the form $t^\alpha |x|^\sigma$ is considered in front of the power nonlinearity. Two types of non-homogeneous boundary conditions are investigated...

This note is concerned with some inequalities involving the function and its Caputo‐type Erdélyi–Kober fractional derivative. Namely, we establish integral inequalities of Poincaré, Sobolev, and Hilbert–Pachpatte types, with respect to the right‐hand sided Caputo‐type modification of the Erdélyi–Kober fractional derivative. The obtained inequalitie...

In this paper, an initial value problem for a nonlinear time-fractional Schr\"odinger equation with a singular logarithmic potential term is investigated. The considered problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Using the test function method with a judicious choice of the test functi...

In this paper, we consider a two-times nonlinear fractional differential inequality involving both Hadamard-Caputo and Caputo fractional derivatives of different orders, with a singular potential term. We obtain sufficient criteria depending on the parameters of the problem, for which a global solution does not exist. Some examples are provided to...

We investigate Cauchy problems for two classes of nonlinear Sobolev type equations with potentials defined on complete noncompact Riemannian manifolds. The first one involves a polynomial nonlinearity and the second one involves a gradient nonlinearity. Namely, we derive sufficient conditions depending on the geometry of the manifold, the power non...

We investigate nonlinear elliptic equations of the form \begin{document}$ -\Delta_{H} u(\xi)+ A(\xi) \cdot \nabla_{H} u(\xi) = V(\xi)f(u),\quad \xi\in \mathbb{H}^n, $\end{document} where \begin{document}$ \mathbb{H}^n = (\mathbb{R}^{2n+1},\circ) $\end{document} is the \begin{document}$ (2n+1) $\end{document}-dimensional Heisenberg group, \begin{doc...

We establish necessary conditions for the existence of global weak solutions to a class of semilinear time-fractional wave inequalities with nonlinearity of derivative type, defined on complete noncompact Riemannian manifolds. A potential function depending of both time and space, is allowed in front of the power nonlinearity. The obtained conditio...

We first consider the damped wave inequality ∂2u∂t2−∂2u∂x2+∂u∂t≥xσ|u|p,t>0,x∈(0,L), where L>0, σ∈R, and p>1, under the Dirichlet boundary conditions (u(t,0),u(t,L))=(f(t),g(t)),t>0. We establish sufficient conditions depending on σ, p, the initial conditions, and the boundary conditions, under which the considered problem admits no global solution....

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate...

In this paper, we consider a degenerate hyperbolic inequality in an exterior domain under three types of boundary conditions: Dirichlet-type, Neumann-type, and Robin-type boundary conditions. Using a unified approach, we show that all the considered problems have the same Fujita critical exponent. Moreover, we answer some open questions from the li...

In this paper, we study the nonexistence of global weak solutions to higher-order time-fractional evolution inequalities with subcritical degeneracy. Using the test function method and some integral estimates, we establish sufficient conditions depending on the parameters of the problems so that global weak solutions cannot exist globally.

We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (M,g) of dimension N≥3, without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solut...

We investigate the existence and uniqueness of positive solutions to an integral equation involving convex or concave nonlinearities. A numerical algorithm based on Picard iterations is provided to obtain an approximation of the unique solution. The main tools used in this work are based on partial-ordering methods and fixed-point theory. Our resul...

This study is devoted to the investigation of nonlinear systems of fourth-order boundary value problems. Namely, using some techniques from matrix analysis and ordinary differential equations, a Lyapunov-type inequality providing a necessary condition for the existence of nonzero solutions is obtained. Next, an estimate involving generalized eigenv...

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the...

We consider the fractional elliptic inequality with variable-exponent nonlinearity $$\begin{aligned} (-\Delta )^{\frac{\alpha }{2}} u+\lambda \, \Delta u \ge |u|^{p(x)}, \quad x\in {\mathbb {R}}^N, \end{aligned}$$where \(N\ge 1\), \(\alpha \in (0,2)\), \(\lambda \in {\mathbb {R}}\) is a constant, \(p: {\mathbb {R}}^N\rightarrow (1,\infty )\) is a m...

In this paper, we establish new inequalities in the setting of 2-metric spaces and provide their geometric interpretations. Some of our results are extensions of those obtained by Dragomir and Goşa (J. Indones. Math. Soc. 11(1):33–38, 2005) in the setting of metric spaces.

In this note, we prove the equivalence between a fixed point theorem for ––concave operators and a previous one for generalized concave operators. 1. Introduction In this note, we show that the fixed point result established by Zhai and Wang [1] for ––concave operators is equivalent to a previous result due to Zhai and Wang [2] for generalized con...

In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case.

We investigate the finite time blow-up and global existence of sign-changing solutions to the Cauchy problem for the inhomogeneous semilinear parabolic system with space-time forcing terms{ut−Δu=|v|p+tσw1(x),x∈RN,t>0,vt−Δv=|u|q+tγw2(x),x∈RN,t>0,(u(0,x),v(0,x))=(u0(x),v0(x)),x∈RN,where N≥1, p,q>1, σ,γ>−1, σ,γ≠0, w1,w2≢0, and u0,v0∈C0(RN). For the fi...

We study the wave inequality with a Hardy potential ∂ t t u − Δ u + λ | x | 2 u ≥ | u | p in ( 0 , ∞ ) × Ω , $$\begin{array}{} \displaystyle \partial_{tt}u-{\it\Delta} u+\frac{\lambda}{|x|^2}u\geq |u|^p\quad \mbox{in } (0,\infty)\times {\it\Omega}, \end{array}$$ where Ω is the exterior of the unit ball in ℝ N , N ≥ 2, p > 1, and λ ≥ − N − 2 2 2 $\b...

We investigate the large-time behavior of solutions for a class of inhomogeneous semilinear wave equations involving double damping and potential terms. Namely, we first establish a general criterium for the absence of global weak solutions. Next, some special cases of potential and inhomogeneous terms are studied. In particular, when the inhomogen...

We consider the differential inequality with a nonlinear memory ∂tu−Δu≥1Γ(σ)∫0t(t−s)σ−1|u(s,x)|pds+w(x),t>0,x∈R+N, where N≥2, p>1, σ>0, and w⁄≡0. Under certain conditions on the initial value and the inhomogeneous term w, we show that the Fujita critical exponent is given by pσ∗=∞, for all σ>0. Next, we consider the limit case of the above problem...

This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansi...

A system of integral equations related to an epidemic model is investigated. Namely, we derive sufficient conditions for the existence and uniqueness of global solutions to the considered system. The proof is based on Perov’s fixed point theorem and some integral inequalities. 1. Introduction Many phenomena related to infectious diseases can be mo...

In this paper, a nonlinear integral equation related to infectious diseases is investigated. Namely, we first study the existence and uniqueness of solutions and provide numerical algorithms that converge to the unique solution. Next, we study the lower and upper subsolutions, as well as the data dependence of the solution. 1. Introduction We cons...

In this paper, we are concerned with the well-posedness of a fractional model of human immunodeficiency virus infection. Namely, using Grönwall’s lemma and Perov’s fixed point theorem, we obtain sufficient conditions for which the considered model admits a unique solution. 1. Introduction The human immunodeficiency virus (HIV) is one of the world’...

This work is motivated essentially by the success of the applications of the nonsingular Yang–Abdel–Aty–Cattani (YAC) derivative in many research area of science, engineering, and financial mathematics. Furthermore, the major determination of this survey work is to achieve Fourier transform of the aforesaid new operator. Obviously, the Cauchy‐react...

The Lotka-Volterra model is a very famous model and frequently used to describe the dynamics of ecological systems in which two species interact, one a predator and one its prey. In this present work, a comparative study is presented for solving Lotka-Volterra model which has an important role in Biological sciences. The Lotka-Volterra equations ar...

We study the nonexistence of global solutions for new classes of nonlinear fractional differential inequalities. Namely, sufficient conditions are provided so that the considered problems admit no global solutions. The proofs of our results are based on the test function method and some integral estimates. 1. Introduction We first consider the pro...

The objective of this paper is to establish -analogue of some well-known inequalities in analysis, namely, Poincaré-type inequalities, Sobolev-type inequalities, and Lyapunov-type inequalities. Our obtained results may serve as a useful source of inspiration for future works in quantum calculus. 1. Introduction and Preliminaries Mathematical inequ...

We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,ω)−Δϕ(t,ω)+ϕt(t,ω)=1Γ(1−ρ)∫0t(t−σ)−ρ|ϕ(σ,ω)|qdσ+μ(ω),t>0, ω∈RN imposing the condition (ϕ(0,ω),ϕt(0,ω))=(ϕ0(ω),ϕ1(ω))inRN, where N≥1, q>1, 0<ρ<1, ϕi∈Lloc1(RN), i=0,1, μ∈Lloc1(RN) and μ≢0. Namely, it is shown that, if ϕ0,ϕ1≥0, μ∈L1(RN) and ∫R...

This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrödinger equations of the form iα∂tαω(t,z)+a1(t)Δω(t,z)+iαa2(t)ω(t,z)=ξ|ω(t,z)|p,(t,z)∈(0,∞)×RN, where N≥1, ξ∈C\{0} and p>1, under suitable initial data. To establish our nonexistence theorem, we adopt the Pohozaev nonlinear capacity method, and con...

We study the existence and nonexistence of global weak solutions to the semilinear parabolic differential inequality $$\begin{aligned} \partial _t u-\Delta u \ge |u|^p,\quad (t,x)\in (0,\infty )\times B^c, \end{aligned}$$where \(p>1\), B is the closed unit ball in \({\mathbb {R}}^N\) (\(N\ge 2\)) and \(B^c\) is its complement, under the semilinear...