Everaldo S. Medeiros

Positive and Nodal Solutions For a Nonlinear Schrödinger Equation with Indefinite Potential

Abstract We deal with the nonlinear Schrödinger equation -Δu + V(x)u = f(u) in ℝN, where V is a (possible) sign changing potential satisfying mild assumptions and the nonlinearity f ∈ C1(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 associated functional constrained to Nehari type sets.

Multiplicity of solutions for a class of quasilinear problem in exterior domains with Neumann conditions

We study the existence and multiplicity of solutions for a class of quasilinear elliptic problem in exterior domain with Neumann boundary conditions.

Periodic solutions for nonlinear equations with mean curvature-like operators

Abstract We give an existence result for a periodic boundary value problem involving mean curvature-like operators in the scalar case. Following [R. Manasevich, J. Mawhin, Periodic solutions for nonlinear systems with p -Laplacian-like operators, J. Differential Equations 145 (1998), 367–393], we use an approach based on the Leray–Schauder degree.

Hamiltonian elliptic systems with nonlinearities of arbitrary growth

We study the existence of standing wave solutions for the following class of elliptic Hamiltonian-type systems: \[ \begin{cases} -\hs^2\Delta u+ V(x)u = g(v) & \mbox{in } \mathbb{R}^N, \\ -\hs^2\Delta v+ V(x)v = f(u) & \mbox{in } \mathbb{R}^N, \end{cases} \] with

On a class of nonhomogeneous elliptic problems involving exponential critical growth

N\geq2

On a Class of Semilinear Elliptic Eigenvalue Problems in ℝ 2

, where

An Elliptic Equation Involving Exponential Critical Growth in ℝ2

\hbar

A Note on the Existence of a Positive Solution for a Non-autonomous Schrödinger–Poisson System

is a positive parameter and the nonlinearities

Nonexistence of positive classical solutions for the nonlinear Schrödinger equation with unbounded or decaying weights

f,g

ON A CLASS OF ELLIPTIC SYSTEM OF SCHRÖDINGER–POISSON TYPE

are superlinear and can have arbitrary growth at infinity. This system is in variational form and the associated energy functional is strongly indefinite. Moreover, in view of unboundedness of the domain