Multiplicity of semiclassical states for fractional Schrodinger equations with critical frequency

被引：0
|
作者：
Zhang, Hui [1 ]
Zhang, Fubao [2 ]
机构：
[1] Jinling Inst Technol, Dept Math, Nanjing 211169, Jiangsu, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 190卷
基金：
中国国家自然科学基金;
关键词：
Fractional Schrodinger equation; Variational method; Critical frequency; Critical growth; High energy solution; GROUND-STATES;
D O I：
10.1016/j.na.2019.111599
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We are concerned with the fractional Schrodinger equation epsilon(2 alpha)(-Delta)(alpha)u + V(x)u = u vertical bar u vertical bar(2)*alpha(-2)u, x is an element of R-N, where epsilon > 0 is a parameter, 0 < alpha < 1, N >= 3, 2(alpha)* = 2N/N-2 alpha, V is an element of L-N/2 alpha(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. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：15
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