Publications (25)18.68 Total impact
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ABSTRACT: We establish existence of a positive solution to the stationary nonlinear Schrödinger equation Δu+V(x)u=f(u), u∈H¹(R^{N}), in situations where this problem does not have a ground state. We consider general superlinear nonlinearities and asymptotically linear ones, as well. Key words: Nonlinear Schrödinger equation; asymptotically linear; superlinear; positive solution; variational methods. MSC2010: 35Q55 (35B09, 35J20).  [Show abstract] [Hide abstract]
ABSTRACT: We consider the nonlinear SchrÖdinger equation Δu + V(x)u = f (x, u), x ∈ RN, where V is invariant under an orthogonal involution and converges to a positive constant as x → +∞ and the nonlinearity f is asymptotically linear at infinity. Existence of a positive solution, as well as some results on the existence of a class of signchanging solutions is presented. The new idea is to use the projection on the Pohozaev manifold associated with the problem at infinity in order to show that a minmax energy level is in the appropriate range for compactness.Advanced Nonlinear Studies 02/2015; 15(1):191219. · 0.92 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The aim of this paper is to present a signchanging solution for a class of radially symmetric asymptotically linear Schrödinger equations. The proof is variational and the Ekeland variational principle is employed as well as a deformation lemma combined with Miranda’s theorem.Proceedings of the Edinburgh Mathematical Society 01/2015; 1:120. DOI:10.1017/S0013091514000339 · 0.48 Impact Factor 
Article: Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities
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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.Nonlinear Analysis 05/2014; 116. DOI:10.1016/j.na.2014.09.030 · 1.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the existence of nonnegative solutions for a nonlinear problem involving the fractional pLaplacian operator. The problem is set on a unbounded domain, and compactness issues have to be handled.  [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 · 0.61 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a new method for finding positive solutions of nonlinear elliptic equations, which are nonhomogeneous 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 · 1.32 Impact Factor  [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(12). DOI:10.1007/s005260110484x · 1.52 Impact Factor  [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 · 0.84 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.Advanced Nonlinear Studies 01/2012; 12(1). · 0.92 Impact Factor  [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)35J61–35J20–47J30Milan Journal of Mathematics 06/2011; 79(1):259271. DOI:10.1007/s0003201101458 · 0.66 Impact Factor 
Article: A note on existence of antisymmetric solutions for a class of nonlinear Schrödinger equations
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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)35J60–35D05–35J20–47J30Zeitschrift für angewandte Mathematik und Physik ZAMP 02/2011; 62(1):6786. DOI:10.1007/s0003301000707 · 1.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this article, we consider the nonlinear Schrödinger equation Δu+V(x)u=u p1 u in ℝ N · Here V is invariant under an orthogonal involution. The basic tool employed here is the concentrationcompactness principle. A theorem on existence of a solution which changes sign exactly once is given.Differential and Integral Equations 01/2011; 24(1/2). · 0.86 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 signchanging solution under a double power growth condition on the nonlinearity.Advances in Differential Equations 01/2010; 15(1/2). · 1.01 Impact Factor  [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 articleAdvanced Nonlinear Studies 09/2008; 10(3). · 0.92 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper orbital stability of solutions of weakly coupled nonlinear Schrödinger equations is studied. It is proved that ground state solutionsscalar or vector onesare orbitally stable, 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. 
Article: Positive and nodal solutions for a nonlinear Schrodinger equation with indefinite potential
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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 nonlinearity f ∈ C 1 (R, R) is a subcritical and superlinear function. By combining variational techniques and the concentrationcompactness principle we obtain a positive ground state solution and also a nodal solution. The proofs rely in localizing the infimum of the associated functional constrained to Nehari type sets.Advanced Nonlinear Studies 01/2008; 8:353373. · 0.92 Impact Factor  [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 11/2007; 14(34). DOI:10.1007/s0003000750397 · 0.90 Impact Factor  [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(2229):743767. DOI:10.1016/j.jde.2006.07.002 · 1.68 Impact Factor  [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 infinity. 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(78). DOI:10.1081/PDE120005847 · 1.01 Impact Factor
Publication Stats
252  Citations  
18.68  Total Impact Points  
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Institutions

20022014

University of Brasília
 Department of Mathematics
Brasília, Federal, Brazil
