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 ${\lambda }_0>0$ such that for any $\lambda \in \left(0,{\lambda }_0\right)$, 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.