带有超线性项或次线性项的Schrödinger-Poisson系统解的存在性和多重性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 668-682.

带有超线性项或次线性项的Schrödinger-Poisson系统解的存在性和多重性

叶一蔚, 唐春雷

西南大学数学与统计学院, 重庆 400715;
2 重庆师范大学数学学院, 重庆 401331

收稿日期:2014-06-04 修回日期:2014-10-21 出版日期:2015-08-25 发布日期:2015-08-25
作者简介:唐春雷, tangcl@swu.edu.cn, tangcl8888@sina.com
基金资助:
家自然科学基金(11471267)和重庆师范大学基金项目(14XLB008)资助

Existence and Multiplicity Results for Schrödinger-Poisson System with Superlinear or Sublinear Terms

Ye Yiwei, Tang Chunlei

1 School of Mathematics and Statistics, SouthwestUniversity, Chongqing 400715;
2 College of Mathematics Science, Chongqing NormalUniversity, Chongqing 401331

Received:2014-06-04 Revised:2014-10-21 Online:2015-08-25 Published:2015-08-25

摘要/Abstract

摘要：

该文研究如下Schrödinger-Poisson系统解的存在性和多重性
其中V∈ C(R³, R)并且K∈ L²∪ L^∞满足K≥ 0.在没有Ambrosetti-Rabinowitz型超二次条件以及映射t→(f(x,t))/(t³)的单调性假设下,利用对称山路引理证明了无穷多个高能量解的存在性. 此外,考虑了非线性项f次线性增长的情形并获得了解的存在性和多重性.s

关键词: dinger-Poisson系统, 超线性, 次线性, 无穷多解, 变分方法

Abstract:

In this paper, we study the existence and multiplicity of solutions for the Schrödinger-Poisson system
where V∈ C(R³, R) and K∈ L²∪ L^∞ with K≥ 0. Without assuming the Ambrosetti-Rabinowitz type superquadratic condition and the monotonicity of the function t→(f(x,t))/(t³), we prove the existence of infinitely many high-energy solutions by using symmetric mountain pass theorem. We also consider the case where f is sublinear and establish the existence and multiplicity.

Key words: Schrö, dinger-Poisson system, Superlinear, Sublinear, Infinitely many solutions, Variational methods

中图分类号:

O176.3

叶一蔚, 唐春雷. 带有超线性项或次线性项的Schrödinger-Poisson系统解的存在性和多重性[J]. 数学物理学报, 2015, 35(4): 668-682.

Ye Yiwei, Tang Chunlei. Existence and Multiplicity Results for Schrödinger-Poisson System with Superlinear or Sublinear Terms[J]. Acta mathematica scientia,Series A, 2015, 35(4): 668-682.

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