数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 1881-1888.doi: 10.1016/S0252-9602(10)60180-4

• 论文 • 上一篇    下一篇

FOUNTAIN THEOREM OVER CONES AND APPLICATIONS

严树森|杨健夫   

  1. Department of Mathematics, The University of New England, Amidale, NSW 2351, Australia;Department of Mathematics, Jiangxi Normal University, Nanchang |330022, China
  • 收稿日期:2010-04-22 出版日期:2010-11-20 发布日期:2010-11-20
  • 基金资助:

    The first author is supported by ARC grant of Australia; the second author is supported by National Natural Sciences Foundations of China (10961016 and 10631030); NSF of Jiangxi (2009GZS0011).

FOUNTAIN THEOREM OVER CONES AND APPLICATIONS

 YAN Shu-Sen, YANG Jian-Fu   

  • Received:2010-04-22 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    The first author is supported by ARC grant of Australia; the second author is supported by National Natural Sciences Foundations of China (10961016 and 10631030); NSF of Jiangxi (2009GZS0011).

摘要:

In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem
{ -Δp u =λ |u|q-2u +μ |uγ-2u,       x∈Ω,
 u = 0,                                             x∈∂Ω,                (1)
 to show that problem (1) possesses infinitely many solutions, where 1<p<N, 1< q <p < γ, Ω(RN is a smooth bounded domain and λ,μ∈R.

关键词: fountain theorem over cones, infinitely , many solutions, quasilinear elliptic problem

Abstract:

In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem
{ -Δp u =λ |u|q-2u +μ |uγ-2u,       x∈Ω,
 u = 0,                                             x∈∂Ω,                (1)
 to show that problem (1) possesses infinitely many solutions, where 1<p<N, 1< q <p < γ, Ω(RN is a smooth bounded domain and λ,μ∈R.

Key words: fountain theorem over cones, infinitely , many solutions, quasilinear elliptic problem

中图分类号: 

  • 35J60