Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity

Abstract

In this article, we study the existence and multiplicity of solutions of the boundary-value problem $$\displaylines{ -\Delta u = f(x,u), \quad \text{in } \Omega, \cr u = 0, \quad \text{on } \partial\Omega, }$$ where $\Delta$ denotes the N-dimensional Laplacian, $\Omega$ is a bounded domain with smooth boundary, $\partial\Omega$, in $\mathbb{R}^N$ $(N\geq 3)$, and f is a continuous function having subcritical growth in the second variable.

Keywords

• semilinear elliptic boundary value problem
• superlinear subcritical growth
• infinite dimensional morse theory
• critical groups