Existence, non-existence and concentration of solutions to some biharmonic problems and systems

Abstract

In this project the author proposes the study of some questions about existence and concentration of solutions to some elliptic partial differential equations involving the biharmonic operator. More specifically, its proposed the study of three problems, in which in two of them the concern is about a stationary version of the Schrödinger biharmonic equation. The first one deals with some questions about the existence of nontrivial solutions, assuming in the nonlinearity f a critical exponential growth condition. In the second one, its proposed the study of at least three nontrivial solutions, including a nodal (sign-changing solution) one. In the last problem, its proposed the study of some results about the well known Lane-Emden conjecture, in which the concern is about nonexistence results to the Lane-Emden system to some specific values of the exponents p and q. (AU)