A multiplicity result for a class of fractional p-Laplacian equations with perturbations in ℝN. Issue 7 (2nd July 2020)

• Record Type: Journal Article
• Authors: Zhang, Xia; Zhang, Binlin
• Is Part Of: Complex variables and elliptic equations. Volume 65:Issue 7(2020)
• Page Start: 1219
• Page End: 1255
• Publication Date: 2020-07-02
• Subjects: V. Radulescu; Fractional Laplacian -- perturbation -- Ekeland's variational principle -- mountain pass theorem; 35A15 -- 35J60 -- 46E35; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2019.1574775
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: This paper deals with a class of nonlinear elliptic equations with perturbations in the whole space involving the fractional p -Laplacian. As a particular case, we investigate the following Schrödinger equations with perturbations: ( − Δ ) p s u + V ( x ) u = g ( x ) f ( u ) + h ( x ) x ∈ R N, where ( − Δ ) p s is the fractional p -Laplacian operator, V ( x ) is a positive continuous function, h ( x ) is a perturbation. We first establish a compactness theorem which allows us to give some estimates of the energy levels where the Palais-Smale condition can fail. Furthermore, using Ekeland's variational principle and the mountain pass theorem, we obtain the existence of at least two distinct nonnegative weak solutions for the above-mentioned equations.