数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (4): 633-638.

• 论文 • 上一篇    下一篇

NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

 韩丕功   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100080, China
  • 出版日期:2004-10-20 发布日期:2004-10-20

NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

 Han Pigong   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100080, China
  • Online:2004-10-20 Published:2004-10-20

摘要:

This paper deals with the Neumann problem for a class of semilinear elliptic equations −u + u = |u|2−2u + μ|u|q−2u in , @u@ = |u|s−2u on @
, where 2 = 2N N−2 ,s = 2(N−1 ) N−2 , 1 < q < 2,N  3, μ > 0,  denotes the unit outward normal to boundary@. By variational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.

关键词: Neumann problem, semilinear elliptic equation, (PS) c condition, critical Sobolev exponent

Abstract:

This paper deals with the Neumann problem for a class of semilinear elliptic equations −u + u = |u|2−2u + μ|u|q−2u in , @u@ = |u|s−2u on @
, where 2 = 2N N−2 ,s = 2(N−1 ) N−2 , 1 < q < 2,N  3, μ > 0,  denotes the unit outward normal to boundary@. By variational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.

Key words: Neumann problem, semilinear elliptic equation, (PS) c condition, critical Sobolev exponent

中图分类号: 

  • 35J65