Multiplicity of semiclassical states for fractional Schrödinger equations with critical frequency. (January 2020)

• Record Type: Journal Article
• Authors: Zhang, Hui; Zhang, Fubao
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35J05 -- 35J50 -- 35J60; Fractional Schrödinger equation -- Variational method -- Critical frequency -- Critical growth -- High energy solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111599
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We are concerned with the fractional Schrödinger equation ϵ 2 α ( − Δ ) α u + V ( x ) u = | u | 2 α ∗ − 2 u, x ∈ R N, where ϵ > 0 is a parameter, 0 < α < 1, N ≥ 3, 2 α ∗ = 2 N N − 2 α, V ∈ L N 2 α ( R N ) is a nonnegative function and V is assumed to be zero in some region of R N, which means it is of the critical frequency case. By virtue of a global compactness lemma, two barycenter functions and Lusternik–Schnirelman theory, we show the multiplicity of high energy semiclassical states.