Double resonant problems which are locally non-quadratic at infinity

Abstract

We establish the existence of a nontrivial solution for a double resonant elliptic problem under a local non-quadraticity condition at infinity and pointwise limits. We also study the existence of a nonzero solution when there is resonance at the first eigenvalue. The first result is obtained as an application of an abstract theorem that establishes the existence of a nontrivial critical point for functionals of class $C^2$ on real Hilbert spaces.

Keywords

• Resonance
• non-quadratic at infinity
• Morse index.