数学物理学报(英文版)

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BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES

刘玥; 王征平   

  1. 中国科学院武汉物理与数学所, 武汉 430071
  • 收稿日期:2005-01-05 修回日期:1900-01-01 出版日期:2007-07-20 发布日期:2007-07-20
  • 通讯作者: 王征平
  • 基金资助:

    This work was supported by NSFC (10571174, 10631030) and CAS(KJCX3-SYW-S03)

BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES

Liu Yue; Wang Zhengping   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of sciences, Wuhan 430071, China
  • Received:2005-01-05 Revised:1900-01-01 Online:2007-07-20 Published:2007-07-20
  • Contact: Wang Zhengping

摘要:

This article considers the equation
2 u =f(x,u)
with boundary conditions either $u|_{\partial\Omega}=\frac{\partial u}{\partial n}|_{\partial\Omega}=0 $ or $u|_{\partial\Omega}=\bigtriangleup
u|_{\partial\Omega}=0$, where $f(x,t)$ is asymptotically linear with respect to t at infinity, and $\Omega$ is a smooth bounded domain in RN, N >4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x,t).

关键词: Biharmonic, mountain pass theorem, asymptotically linear

Abstract:

This article considers the equation
2 u =f(x,u)
with boundary conditions either $u|_{\partial\Omega}=\frac{\partial u}{\partial n}|_{\partial\Omega}=0 $ or $u|_{\partial\Omega}=\bigtriangleup
u|_{\partial\Omega}=0$, where $f(x,t)$ is asymptotically linear with respect to t at infinity, and $\Omega$ is a smooth bounded domain in RN, N >4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x,t).

Key words: Biharmonic, mountain pass theorem, asymptotically linear

中图分类号: 

  • 35J60