GROUND STATES FOR FRACTIONAL SCHR?DINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH

被引：3

作者：

李全清 ^{[1
]}

王文波 ^{[2
]}

滕凯民 ^{[3
]}

吴鲜 ^{[4
]}

机构：

[1] Department of Mathematics, Honghe University

[2] Department of Mathematics and Statistics, Yunnan University

[3] Department of Mathematics, Taiyuan University of Technology

[4] Department of Mathematics, Yunman Normal University

来源：

ActaMathematicaScientia | 2020年 / 40卷 / 01期

关键词：

fractional Schr?dinger equation; fractional magnetic operator; critical growth;

D O I：

暂无

中图分类号：

O411 [物理学的数学方法];

学科分类号：

0701 ;

摘要：

In this article, we study the following fractional Schr?dinger equation with electromagnetic fields and critical growth (-?)Asu + V(x)u = |u|2s*-2u + λf(x, |u|2)u, x ∈ RN,where(-?)Asis the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2s*=2N/(N-2s),f is a continuous function, V ∈ C(RN, R) and A ∈ C(RN, RN) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.

引用

页码：59 / 74

页数：16

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