A remark on fractional p–Kirchhoff problems involving multiple zeros

Abstract

ABSTRACTIn this paper, we study the multiplicity of solutions for a p–Kirchhoff type problem driven by a nonlocal integro-differential operator. As a particular case, we consider the following problem: where is the fractional p–Laplacian, with sp<N, , is a continuous function vanishing in many different points, is a continuous function, and is a Carathéodory function for each . Under some suitable assumptions, we obtain the multiplicity of solutions for the above problem by applying the mountain pass theorem. Moreover, the asymptotic behavior of solutions is also investigated. A distinguished feature of this paper is that the Kirchhoff function M has multiple zeros.