Perturbation methods for nonlocal Kirchhoff–type problems

Abstract

Abstract This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi–nonlocal operator u ↦ M(∥u∥2)(−Δ) su, where M models a Kirchhoff–type coefficient while (−Δ) s denotes the fractional Laplace operator. More precisely, by adapting to our bi–nonlocal framework the variational and topological tools introduced in [16], we establish the existence of infinitely many solutions. The main feature and difficulty of our problems is due to the possible degenerate nature of the Kirchhoff term M.