Liliane A. Maia

University of Brasília, Brasília, Federal, Brazil

Are you Liliane A. Maia?

Claim your profile

Publications (23)15.17 Total impact

  • Proceedings of the Edinburgh Mathematical Society 01/2015; DOI:10.1017/S0013091514000339 · 0.54 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given.
  • Source
    Raquel Lehrer, Liliane A. Maia, Marco Squassina
    [Show abstract] [Hide abstract]
    ABSTRACT: We investigate the existence of nonnegative solutions for a nonlinear problem involving the fractional p-Laplacian operator. The problem is set on a unbounded domain, and compactness issues have to be handled.
  • Source
    Raquel Lehrer, Liliane A. Maia, Marco Squassina
    [Show abstract] [Hide abstract]
    ABSTRACT: By exploiting a variational technique based upon projecting over the Pohozaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrodinger equations having a nonhomogenous nonautonomous asymptotically linear nonlinearity.
    Complex Variables and Elliptic Equations 01/2014; 60(4). DOI:10.1080/17476933.2014.948434 · 0.65 Impact Factor
  • Raquel Lehrer, Liliane A. Maia
    [Show abstract] [Hide abstract]
    ABSTRACT: We present a new method for finding positive solutions of nonlinear elliptic equations, which are non-homogeneous and asymptotically linear at infinity, by using projections on a Pohozaev manifold rather than the Nehari manifold associated with the problem.
    Journal of Functional Analysis 01/2014; 266(1):213–246. DOI:10.1016/j.jfa.2013.09.002 · 1.15 Impact Factor
  • Source
    Liliane de Almeida Maia, Eugenio Montefusco, Benedetta Pellacci
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the existence of solutions for a class of saturable weakly coupled Schrödinger systems. In most of the cases we show that least energy solutions have necessarily one trivial component. In addition sufficient conditions for the existence of a solution with both positive components are found.
    Calculus of Variations 01/2013; 46(1-2). DOI:10.1007/s00526-011-0484-x · 1.53 Impact Factor
  • Source
    L. A.maia, E.montefusco, B.pellacci
    [Show abstract] [Hide abstract]
    ABSTRACT: Existence of radial solutions with a prescribed number of nodes is established, via variational methods, for a system of weakly coupled nonlinear Schrödinger equations. The main goal is to obtain a nodal solution with all vector components not identically zero and an estimate on their energies.
    Communications in Contemporary Mathematics 05/2012; 10(05). DOI:10.1142/S0219199708002934 · 0.74 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper is concerned with the existence of odd homoclinic orbits for the second-order Hamiltonian system q ¨(t)-L(t)q+b(t)V q (q)=0,q∈ℝ N ,t∈ℝ, where, among other assumptions, the functions L, b and V are even. The problem is variational; indeed, its solutions are the critical points of the functional I(q)=1 2∫ -∞ +∞ (|q ˙| 2 +L(t)q·q)dt-∫ -∞ +∞ b(t)V q (q)dt defined on the Sobolev space E=W 1 (ℝ,ℝ N ). The authors find one odd homoclinic by minimizing the action functional I on the manifold N τ =N∩E τ , where N is the Nehari manifold associated to the problem and E τ is the subspace of odd functions belonging to E. In order to overcome the lack of compactness of the problem, they use a version of the concentration-compactness principle of P.-L. Lions.
    Advanced Nonlinear Studies 01/2012; 12(1). · 0.67 Impact Factor
  • L. A. Maia, R. Ruviaro
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider the nonlinear Schrödinger equation -Du + V (x)u = K(x)u3/(1 + u2)-\Delta{u} + V (x)u = K(x)u^3/(1 + u^2) in \mathbb RN{\mathbb {R}^N} , and assume that V and K are invariant under an orthogonal involution. Moreover, V and K converge to positive constants V ∞ and K ∞, as |x| → ∞. We present some results on the existence of a particular type of sign changing solution, which changes sign exactly once. The basic tool employed here is the Concentration–Compactness Principle and the interaction between translated solutions of the corresponding autonomous problem. Mathematics Subject Classification (2010)35J61–35J20–47J30
    Milan Journal of Mathematics 06/2011; 79(1):259-271. DOI:10.1007/s00032-011-0145-8 · 0.82 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this article, we consider the nonlinear Schrödinger equation -Δu+V(x)u=|u| p-1 u in ℝ N · Here V is invariant under an orthogonal involution. The basic tool employed here is the concentration-compactness principle. A theorem on existence of a solution which changes sign exactly once is given.
    Differential and Integral Equations 01/2011; 24(1/2). · 0.54 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider the nonlinear Schrödinger equation -\triangle u + V(x)u = f(u) in \mathbbRN.-\triangle u + V(x)u= f(u)\quad {\rm in}\quad \mathbb{R}^N. We assume that V is invariant under an orthogonal involution and show the existence of a particular type of sign changing solution. The basic tool employed here is the Concentration–Compactness Principle. Mathematics Subject Classification (2000)35J60–35D05–35J20–47J30
    Zeitschrift für angewandte Mathematik und Physik ZAMP 01/2011; 62(1):67-86. DOI:10.1007/s00033-010-0070-7 · 1.21 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we study the existence and multiplicity of solutions for the semilinear elliptic equation $-\Delta u = Q(x)f'(u)$ in an exterior domain with Neumann boundary conditions. We prove the existence of a positive ground state as well as a sign-changing solution under a double power growth condition on the nonlinearity.
    Advances in Differential Equations 01/2010; 15(1/2). · 0.76 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Orbital stability property for weakly coupled nonlinear Schr\"odinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated elliptic problem. In particular, orbitally stable standing waves can be generated by least action solutions, but also by solutions with one trivial component whether or not they are ground states. Moreover, standing waves with components propagating with the same frequencies are orbitally stable if generated by vector solutions of a suitable single Schr\"odinger weakly coupled system, even if they are not ground states. Comment: 21 pages, original article
    Advanced Nonlinear Studies 09/2008; · 0.67 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper orbital stability of solutions of weakly coupled nonlinear Schrödinger equa-tions is studied. It is proved that ground state solutions-scalar or vector ones-are orbitally sta-ble, while bound states with Morse index strictly greater than one are not stable. Moreover, an instability result for large exponent in the nonlinearity is presented.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We deal with the nonlinear Schrödinger equation −∆u + V (x)u = f (u) in R N , where V is a (possible) sign changing potential satisfying mild assumptions and the non-linearity f ∈ C 1 (R, R) is a subcritical and superlinear function. By combining variational techniques and the concentration-compactness principle we obtain a positive ground state solution and also a nodal solution. The proofs rely in localizing the infimum of the associ-ated functional constrained to Nehari type sets.
    Advanced Nonlinear Studies 01/2008; 8:353-373. · 0.67 Impact Factor
  • Source
    Liliane A. Maia, Elves A. B. Silva
    [Show abstract] [Hide abstract]
    ABSTRACT: It is established the existence and multiplicity of solutions for a class of coupled semilinear elliptic systems in ${\mathbb{R}}^{N}$ where none of the potentials are coercive. The main goal is to consider systems where the primitive of the nonlinearity is superquadratic on appropriate directions.
    Nonlinear Differential Equations and Applications NoDEA 01/2007; 14(3-4). DOI:10.1007/s00030-007-5039-7 · 0.97 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Existence of a nontrivial solution is established, via variational methods, for a system of weakly coupled nonlinear Schrödinger equations. The main goal is to obtain a positive solution, of minimal action if possible, with all vector components not identically zero. Generalizations for nonautonomous systems are considered.
    Journal of Differential Equations 10/2006; 229(2-229):743-767. DOI:10.1016/j.jde.2006.07.002 · 1.57 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Existence and multiplicity of solutions are established, via the Variational Method, for a class of resonant semilinear elliptic system in R N under a local nonquadraticity condition at infin-ity. The main goal is to consider systems with coupling where one of the potentials does not satisfy any coercivity condition. The existence of solution is proved under a critical growth condition on the nonlinearity.
    Communications in Partial Differential Equations 01/2002; 27(7-8). DOI:10.1081/PDE-120005847 · 1.19 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper deals with the existence and multiplicity of solutions to a class of resonant semilinear elliptic system in RN. The main goal is to consider systems with coupling where none of the potentials are coercive. The existence of solution is proved under a critical growth condition on the nonlinearity. 1. Introduction. In this article we study the existence and multiplicity of solu- tions for the problem (P) ( ¡¢u + a(x)u = Fu(x;u;v); x 2RN; ¡¢v + b(x)v = Fv(x;u;v); x 2RN; with N ‚ 3 and the potentials a and b satisfy (A1) there are constants a0;b0 > 0 such that a(x) ‚ a0;b(x) ‚ b0 for all x 2RN, (A2) "(fx 2RN : a(x)b(x) < Mg) < 1; for every M > 0. Here " denotes the Lebesgue measure in RN. We also suppose that the system is
    Discrete and Continuous Dynamical Systems 01/2002; 2003. · 0.92 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The authors establish via variational methods the existence and multiplicity of solutions for a class of semilinear elliptic equations in ℝ n : -Δu+b(x)u=f(x,u),x∈ℝ n , where n≥3 and the potential b is a continuous function satisfying b(x)≥b 0 >0 for all x∈ℝ n . The main goal of the paper is to explore the compactness provided by the condition on the potential, to study a class of double resonant problems under a local nonquadraticity condition. For the existence of solution the nonlinearity may satisfy a critical growth condition. Related results can be found [P. H. Rabinowitz, Z. Angew. Math. Phys. 43, 270–291 (1992; Zbl 0763.35087)].Reviewer: Nicolae Pop (Baia Mare)
    Differential and Integral Equations 01/2002; 15(11). · 0.54 Impact Factor