Multiplicity of Nontrivial Solutions of a Class of Fractional $p$-Laplacian Problem

Abstract

. In this paper, we deal with existence of nontrivial solutions to the fractional p -Laplacian problem of the type where Ω is a bounded domain in R n with smooth boundary ∂ Ω, a ∈ C (Ω), p ≥ 2, α ∈ (0 , 1) such that pα < n , 1 < q < p < r < npn − αp , and F ∈ C 1 (Ω × R , R ). Using the decomposition of the Nehari manifold, we prove that the non-local elliptic problem has at least two nontrivial solutions.