POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM

doi:10.1007/s10473-020-0523-9

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1585-1601.doi: 10.1007/s10473-020-0523-9

POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM

段雪亮¹, 魏公明², 杨海涛³

1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

收稿日期:2018-11-21 修回日期:2019-12-02 出版日期:2020-10-25 发布日期:2020-11-04
通讯作者: Xueliang DUAN E-mail:xueliangduan@outlook.com
作者简介:Gongming WEI,E-mail:gmweixy@163.com;Haitao YANG,E-mail:htyang@zju.edu.cn

POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM

Xueliang DUAN¹, Gongming WEI², Haitao YANG³

1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Received:2018-11-21 Revised:2019-12-02 Online:2020-10-25 Published:2020-11-04
Contact: Xueliang DUAN E-mail:xueliangduan@outlook.com

摘要/Abstract

摘要： We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we prove the existence and nonexistence of ground state solutions for the system with close-to-periodic potentials.

中图分类号:

35A15

段雪亮, 魏公明, 杨海涛. POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM[J]. 数学物理学报(英文版), 2020, 40(5): 1585-1601.

Xueliang DUAN, Gongming WEI, Haitao YANG. POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1585-1601.

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POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM

POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM

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