数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 227-233.

• 论文 • 上一篇    下一篇

含有共振项的p-Laplace方程解的存在性

曾小雨, 万俊霞   

  1. 中国科学院武汉物理与数学研究所 武汉 430071
  • 收稿日期:2013-05-07 修回日期:2013-12-16 出版日期:2014-04-25 发布日期:2014-04-25
  • 基金资助:

    国家自然科学基金(11071245, 11101418, 11271360)资助.

The Existence of |Solution for p-Laplace Equation Involving Resonant Term

 ZENG Xiao-Yu, WAN Jun-Xia   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, |Wuhan 430071
  • Received:2013-05-07 Revised:2013-12-16 Online:2014-04-25 Published:2014-04-25
  • Supported by:

    国家自然科学基金(11071245, 11101418, 11271360)资助.

摘要:

主要讨论一类非线性项在无穷远处渐近|u|p-2u 增长的p-Laplace方程的Dirichlet边值问题, 利用环绕定理证明了当 λ1λ<λ2 (λ1为算子(-?p, W1, p0(Ω) )第一特征值)时, 方程存在非平凡解.

关键词: 渐近, u, p-2u 增长, p-Laplace方程, 环绕定理

Abstract:

In this paper, a class of p-Laplace equations involving  a term of asymptotically |u|p-2u at infinity  are studied under the Dirichlet boundary condition. By applying the  linking theorem, the existence of nontrivial solution is obtained  when  λ1λ<λ2 , where λ1 is the first eigenvalue of (-?p, W1, p0(Ω) ).

Key words: Asymptotically , u, p-2u, p-Laplace equation, Linking theorem

中图分类号: 

  • 35J20