Multiplicity of Solutions for Dirichlet Problem of a Superlinear Fractional p-Laplacian Equation

Abstract

This paper is dedicated to studying the following fractional p-Laplacian problem where Ω⊂ℝN (N ≥ 2) is a bounded domain with C 1,1 boundary, s∈(0,1), 2 ≤ p<N/s, (-Δ) s p is the fractional p-Laplacian and f is a (p-1)-superlinear Carathéodory reaction but does not satisfy the usual Ambrosetti-Rabinowitz condition. By using variational methods and Morse theory, we show that the equation has at least three nontrivial solutions: among one of them is positive and one is negative