Existence and multiplicity results for nonlinear elliptic problems in $R^N$ with an indefinite functional

Abstract

We prove the existence of a nontrivial solution for the nonlinear elliptic problem $-Delta u=lambda h(x)u + a(x)g(u)$ in $R^N$, where $g$ is superlinear near zero and near infinity, $a(x)$ changes sign, $lambda $ is positive, and $h(x)geq 0$ is a weight function. For $g$ odd, we prove the existence of an infinite number of solutions.

Keywords

• Superlinear elliptic problems
• Morse index
• minimax methods.