Elves A. B. Silva

Multiplicity of solutions for quasilinear elliptic problems involving critical sobolev exponents

Abstract The main results of this paper establish, via the variational method, the multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents under the presence of symmetry. The concentration-compactness principle allows to prove that the Palais–Smale condition is satisfied below a certain level.

Existence and multiplicity of solutions for semilinear elliptic systems

In this article, it is considered the existence of nonzero solutions for a semilinear elliptic system. First, the existence of one nonzero solution is obtained by applying a version of the generalized mountain pass theorem. Next, a maximum principle is used to derive the existence of a positive and a negative solution. Finally, the generalized Morse theory is used to provides the exist ence of at least three nonzero solutions when the primitive of the nonlinearity has a superquadratic behaviour at infinity.In this article, it is considered the existence of nonzero solutions for a semilinear elliptic system. First, the existence of one nonzero solution is obtained by applying a version of the generalized mountain pass theorem. Next, a maximum principle is used to derive the existence of a positive and a negative solution. Finally, the generalized Morse theory is used to provides the exist ence of at least three nonzero solutions when the primitive of the nonlinearity has a superquadratic behaviour at infinity.

SOLUTIONS FOR A RESONANT ELLIPTIC SYSTEM WITH COUPLING IN

ABSTRACT Existence and multiplicity of solutions are established, via the Variational Method, for a class of resonant semilinear elliptic system in 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.

A version of Rolle's theorem and applications

This paper deals with global injectivity of vector fields defined on euclidean spaces. Our main result establishes a version of Rolles Theorem under generalized Palais-Smale conditions. As a consequence of this, we prove global injectivity for a class of vector fields defined on n-dimensional spaces.

Systems with coupling in

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.