数学物理学报 ›› 2013, Vol. 33 ›› Issue (1): 174-184.

• 论文 • 上一篇    

RN中一类拟线性椭圆方程组非负解的存在性和多重性

张文丽1|钟立楠2**   

  1. 1.长治学院数学系 山西长治 046011;
     2.延边大学理学院数学系 吉林延吉 133002
  • 收稿日期:2011-11-30 修回日期:2012-12-08 出版日期:2013-02-25 发布日期:2013-02-25
  • 通讯作者: 钟立楠, E-mail:ywl6133@126.com; zhonglinan2000@126.com
  • 基金资助:

    国家自然科学基金(10771105)和山西省高校科技研究开发项目(20111129)资助

Existence and Multiplicity of Nonnegative Solutions for a Quasilinear System in RN

 ZHANG Wen-Li1, ZHONG Li-Nan2**   

  1. 1.Department of Mathematics, Changzhi University, Shanxi Changzhi |046011;
    2.Department of Mathematics, College of Science, Yanbian University, Jilin Yanji 133002
  • Received:2011-11-30 Revised:2012-12-08 Online:2013-02-25 Published:2013-02-25
  • Contact: ZHONG Li-Nan, E-mail:ywl6133@126.com; zhonglinan2000@126.com
  • Supported by:

    国家自然科学基金(10771105)和山西省高校科技研究开发项目(20111129)资助

摘要:

利用极小极大原理和Ljusternik-Schnirelmann 畴数理论, 研究了RN中一类拟线性椭圆方程组. 当2≤p, q<N时, α≥0, β≥0 满足α+β+2>max{p, q}和α+1/p*+β+1/q* ≤1, 通过建立解的个数与正连续函数VW达到极小值集合的拓扑量之间的关系, 得到拟线性方程组至少存在catMδ(M)个不同的非负解.

关键词: 拟线性方程组, Nehari 流形, 极小极大原理, Ljusternik-Schnirelmann 畴数理论

Abstract:

In this paper, we consider a class of quasilinear elliptic equations in RN by the minimax theorems and the Ljusternik-Schnirelmann
theory. When 2≤p, q<N, α≥0 and β≥0 satisfy the conditions of α+β+2>max{p, q} and α+1/p*+β+1/q* ≤1, the quasilinear system has at least catMδ(M)  nonnegative solutions by relating the number of solutions with the topology of the set where V and W attain its minimum.

Key words: Quasilinear system,  Nehari manifold, Minimax theorems, Ljusternik-Schnirelmann theory

中图分类号: 

  • 34B15