On fractional p-Laplacian type equations with general nonlinearities

Abstract

In this paper, we study the existence and multiplicity of solutions for a class of quasi-linear elliptic problems driven by a nonlocal integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study the following problem: { (−∆)s pu = f(x, u) in Ω, u = 0 in R N Ω, where (−∆)s p is the fractional p-Laplacian operator, Ω is an open bounded subset of R N with Lipschitz boundary and f : Ω × R → R is a generic Carathéodory function satisfying either a p−sublinear or a p−superlinear growth condition.