Existence of weak solutions for a class of fractional Schrödinger equations with periodic potential. (1st February 2017)

• Record Type: Journal Article
• Authors: Pu, Yang; Liu, Jiu; Tang, Chun-Lei
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 3(2017)
• Page Start: 465
• Page End: 482
• Publication Date: 2017-02-01
• Subjects: Nonlinear Schrödinger equation -- Fractional Laplacian -- Strongly indefinite functional; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.12.004
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider a time-independent fractional Schrödinger equation ( − △ ) α u + V ( x ) u = f ( x, u ) in R N, u ∈ H α ( R N ), where α ∈ ( 0, 1 ), N > 2 α, V ( x ) is a periodic potential, f is superlinear and has a general subcritical growth. Based on a generalized linking theorem and a variant fountain theorem for strongly indefinite functional, we obtain a ground state solution and infinitely many solutions.