Degenerate Kirchhoff problems involving the fractional p-Laplacian without the (AR) condition

Abstract

In this paper, we use a variant of the mountain pass theorem to investigate the existence of nontrivial solutions for a degenerate Kirchhoff type problem driven by a nonlocal fractional -Laplace operator with homogeneous Dirichlet boundary conditions:where , is a smooth bounded domain of , is the fractional -Laplace operator with and , and is a Carathéodory function. The main feature of this paper is the fact that the coefficient of fractional Laplace operator can be zero at zero, that is, the problem is degenerate. The novelty here is that we may consider nonlinearities that satisfy a local -superlinear condition and may change sign.