Variational Approach for the Variable-Order Fractional Magnetic Schrödinger Equation with Variable Growth and Steep Potential in ℝ N ∗
Variational Approach for the Variable-Order Fractional Magnetic Schrödinger Equation with Variable Growth and Steep Potential in ℝ N ∗
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DOI：
10.1155/2020/1320635
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发表时间：
2020-10
影响因子：
1.2
通讯作者：
Jianwen Zhou;Bianxiang Zhou;L. Tian;Yanning Wang
中科院分区：
文献类型：
--
作者：
Jianwen Zhou;Bianxiang Zhou;L. Tian;Yanning Wang
本文证明了一类由变阶分数阶拉普拉斯算子驱动的具有变指数和陡势的不定分数阶薛定谔方程解的存在性。在适当的条件下，利用Nehari流形的分解和变分方法，得到了该方程非平凡解的存在性结果。
In this paper, we show the existence of solutions for an indefinite fractional Schrödinger equation driven by the variable-order fractional magnetic Laplace operator involving variable exponents and steep potential. By using the decomposition of the Nehari manifold and variational method, we obtain the existence results of nontrivial solutions to the equation under suitable conditions.