Resonant problems for non-local elliptic operators with unbounded nonlinearites

Abstract

In this paper we study the existence of nontrivial solutions of a class of asymptotically resonant problems driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions by applying Morse theory and critical groups for a $ C^{2} $ functional at both isolated critical points and infinity.

Keywords

• integro-differential operator
• variational methods
• resonance
• critical group
• morse theory