MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL

doi:10.1016/S0252-9602(17)30021-8

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 555-572.doi: 10.1016/S0252-9602(17)30021-8

• 论文 • 上一篇

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL

王丽霞^1,2, 马世旺³, 许娜⁴

1. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China;
2. School of Sciences, Tianjin Chengjian University, Tianjin 300384, China;
3. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;
4. School of Sciences, Tianjin University of Technology and Education, Tianjin 300222, China

收稿日期:2015-09-28 修回日期:2016-10-08 出版日期:2017-04-25 发布日期:2017-04-25
作者简介:Lixia WANG,E-mail:wanglixia0311@126.com;Shiwang MA,E-mail:shiwangm@163.net;Na XU,E-mail:weila319@163.com
基金资助:
The first author is supported by the Tianyuan Special Foundation (11526148) and the second author is supported by the National Natural Science Foundation of China (11571187)

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL

Lixia WANG^1,2, Shiwang MA³, Na XU⁴

1. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China;
2. School of Sciences, Tianjin Chengjian University, Tianjin 300384, China;
3. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;
4. School of Sciences, Tianjin University of Technology and Education, Tianjin 300222, China

Received:2015-09-28 Revised:2016-10-08 Online:2017-04-25 Published:2017-04-25
Supported by:
The first author is supported by the Tianyuan Special Foundation (11526148) and the second author is supported by the National Natural Science Foundation of China (11571187)

摘要/Abstract

摘要：

In this article,we study the following nonhomogeneous Schrödinger-Poisson equations

where λ > 0 is a parameter.Under some suitable assumptions on V,K,f and g,the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.In particular,the potential V is allowed to be signchanging.

关键词: Nonhomogeneous, sign-changing potential, Schrödinger-Poisson equations, Ekeland's variational principle, Mountain Pass Theorem

Abstract:

Key words: Nonhomogeneous, sign-changing potential, Schrödinger-Poisson equations, Ekeland's variational principle, Mountain Pass Theorem

王丽霞, 马世旺, 许娜. MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL[J]. 数学物理学报(英文版), 2017, 37(2): 555-572.

Lixia WANG, Shiwang MA, Na XU. MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL[J]. Acta mathematica scientia,Series B, 2017, 37(2): 555-572.

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MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL

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