数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1495-1509.doi: 10.1016/S0252-9602(14)60099-0

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MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

尚月赟|王莉*   

  1. Department of Mathematics, Huazhong Normal University, Wuhan 430074, China;Department of Mathematics, South-Central University for Nationalities, Wuhan 430074, China; School of Basic Science, East China Jiaotong University, Nanchang 330013, China
  • 收稿日期:2013-04-03 修回日期:2013-11-22 出版日期:2014-09-20 发布日期:2014-09-20
  • 通讯作者: 王莉,wangli.423@163.com E-mail:shangyueyun1980@163.com;wangli.423@163.com
  • 基金资助:

    This work was supported by the National Natural Science Foundation of China (11326139, 11326145), Tian Yuan Foundation (KJLD12067), Central Specialized Fundation of SCUEC (CZQ13013), and the Project of Jiangxi Province Technology Hall (2014BAB211010).

MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

 SHANG Yue-Yun, WANG Li*   

  1. Department of Mathematics, Huazhong Normal University, Wuhan 430074, China;Department of Mathematics, South-Central University for Nationalities, Wuhan 430074, China; School of Basic Science, East China Jiaotong University, Nanchang 330013, China
  • Received:2013-04-03 Revised:2013-11-22 Online:2014-09-20 Published:2014-09-20
  • Contact: WANG Li,wangli.423@163.com E-mail:shangyueyun1980@163.com;wangli.423@163.com
  • Supported by:

    This work was supported by the National Natural Science Foundation of China (11326139, 11326145), Tian Yuan Foundation (KJLD12067), Central Specialized Fundation of SCUEC (CZQ13013), and the Project of Jiangxi Province Technology Hall (2014BAB211010).

摘要:

In this paper, we are concerned with the following problem:
{(−Δ)kuλf(x)|u|q−2u + g(x)|u|k*−2u, ∈Ω,
Hk0 (Ω),
where Ω is a bounded domain in RN with N ≥ 2k + 1, 1 < q < 2, λ > 0, f, g are continuous functions on which are somewhere positive but which may change sign on Ω. k* = 2N/N−2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.

关键词: nontrivial solutions, polyharmonic problems, critical exponents, variational methods

Key words: nontrivial solutions, polyharmonic problems, critical exponents, variational methods

中图分类号: 

  • 35B33