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. 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 WANG1,2, Shiwang MA3, Na XU4   

  1. 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:

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:

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.

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