Multiple solutions for the fractional $p$-Laplacian equation with Hardy–Sobolev exponents

Abstract

We study the fractional p-Laplacian problem with Hardy–Sobolev exponents. We prove: there is a λ0>0 such that for any λ∈(0,λ0), the above problem possesses infinitely many solutions. We achieve our goal by making use of variational methods, more specifically, the Nehari manifold and Lusternik–Schnirelmann theory.