文章基本信息

标题：Infinitely many high energy solutions for fractional Schrödinger equations with magnetic field
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作者：Libo Yang ; Tianqing An ; Jiabin Zuo 等
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2019
卷号：2019
期号：1
页码：1-11
DOI：10.1186/s13661-019-01309-z
出版社：Hindawi Publishing Corporation
摘要：In this paper we investigate the existence of infinitely many solutions for nonlocal Schrödinger equation involving a magnetic potential $$ (-\triangle )_{A}^{s}u+V(x)u=f\bigl(x, \vert u \vert \bigr)u, \quad\text{in } {\mathbb {R}}^{N}, $$ where $s\in (0,1)$ is fixed, $N>2s$, $V:{\mathbb {R}}^{N}\rightarrow {\mathbb {R}}^{+}$ is an electric potential, the magnetic potential $A:{\mathbb {R}}^{N}\rightarrow {\mathbb {R}}^{N}$ is a continuous function, and $(-\triangle )_{A}^{s}$ is the fractional magnetic operator. Under suitable assumptions for the potential function V and nonlinearity f, we obtain the existence of infinitely many nontrivial high energy solutions by using the variant fountain theorem..
关键词：Schrödinger equation ; Fractional magnetic operator ; Variant fountain theorem ;