Critical stationary Kirchhoff equations in ${\mathbb{R}}^N$ involving nonlocal operators

Abstract

In this paper we establish existence and multiplicity of nontrivial non-negative entire (weak) solutions of a stationary Kirchhoff eigenvalue problem, involving a general nonlocal integro-differential operator. The model under consideration depends on a real parameter $\Lambda$ and involves two superlinear nonlinearities, one of which could be critical or even supercritical.