引用本文:贺书文, 商彦英.一类带有周期位势的分数阶耦合系统的正基态解[J].西南大学学报(自然科学版),2019,41(2):64~69
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一类带有周期位势的分数阶耦合系统的正基态解
贺书文, 商彦英
西南大学 数学与统计学院, 重庆 400715
摘要:
运用Ekeland变分原理研究了一类带有不同周期位势的分数阶耦合系统非平凡解的存在性.证明了该系统存在的非平凡解可以是一个正基态解,该结果将一般的Schrödinger耦合系统推广到带有多个不同周期函数的分数阶耦合系统的情形.
关键词:  分数阶耦合系统  Ekeland变分原理  正基态解
DOI:10.13718/j.cnki.xdzk.2019.02.010
分类号:O176.3
基金项目:国家自然科学基金项目(11471267).
Positive Ground State Solutions for a Class of Fractional Coupled System with Periodic Potentials
HE Shu-wen, SHANG Yan-ying
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Abstract:
In this article, we investigate the existence of nontrivial solutions for a class of fractional coupled system with different periodic potentials by using the Ekeland's variational principle. The point is to prove that the nontrivial solutions of the system can be a positive ground state solution, which extends the general Schrödinger coupled system to the case of the fractional coupled system with multiple different periodic functions.
Key words:  fractional coupled system  Ekeland's variational principle  positive ground state solution
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