PERTURBATION METHODS FOR NONLOCAL KIRCHHOFF-TYPE PROBLEMS

This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi-nonlocal operator u bar right arrow M(parallel to u parallel to(2))(-Delta)(s)u, where M models a Kirchhoff-type coefficient while (-Delta)(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.