Multiple solutions of nonlinear Schrödinger equation with the fractional Laplacian. (August 2016)

• Record Type: Journal Article
• Authors: Ge, Bin
• Is Part Of: Nonlinear analysis. Volume 30(2016)
• Page Start: 236
• Page End: 247
• Publication Date: 2016-08
• Subjects: Fractional Laplacian -- Infinitely many solutions -- Nonlinear Schrödinger equation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we are devoted to a time-independent fractional Schrödinger equation ( − Δ ) α u + V ( x ) u = f ( x, u ) in R N, where ( − Δ ) α stands for the fractional Laplacian of order α ∈ ( 0, 1 ), f is either asymptotically linear or superquadratic growth. Under appropriate assumptions on V and f, we prove the existence of infinitely many nontrivial high or small energy solutions, which extend and complement previously known results in the literature.