Infinitely many solutions for fourth-order elliptic equations

被引：68
|
作者：
Ye, Yiwei [1 ]
Tang, Chun-Lei [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 394卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Fourth-order elliptic equation; Critical point; Cerami sequences; Symmetric mountain pass theorem; VARIANT FOUNTAIN THEOREMS; SIGN-CHANGING SOLUTIONS; NONTRIVIAL SOLUTIONS; BIHARMONIC-EQUATIONS; TRAVELING WAVES; R-N; R(N);
D O I：
10.1016/j.jmaa.2012.04.041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a class of fourth-order elliptic equations setting on R-N. Based on the minimax methods in critical point theory, we obtain the existence of infinitely many large-energy and small-energy solutions, which unifies and improves the recent results of Yin and Wu [Y. Yin, X. Wu, High energy solutions and nontrivial solutions for fourth-order elliptic equations, J. Math. Anal. Appl. 375 (2011)699-705]. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：841 / 854
页数：14
相关论文
共 50 条
  • [41] Boundary decay estimates for solutions of fourth-order elliptic equations
    Barbatis, Gerassimos
    [J]. ARKIV FOR MATEMATIK, 2007, 45 (02): : 197 - 219
  • [42] Existence and multiplicity of solutions for fourth-order elliptic equations in RN
    Ye, Yiwei
    Tang, Chun-Lei
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 406 (01) : 335 - 351
  • [43] Infinitely many solutions for a fourth-order differential equation on a nonlinear elastic foundation
    Xiaodan Wang
    [J]. Boundary Value Problems, 2013
  • [44] Infinitely many solutions for a fourth-order differential equation on a nonlinear elastic foundation
    Wang, Xiaodan
    [J]. BOUNDARY VALUE PROBLEMS, 2013,
  • [45] INFINITELY MANY SOLUTIONS FOR PERTURBED FOURTH-ORDER KIRCHHOFF-TYPE PROBLEMS
    Nazari, Abdollah
    Afrouzi, Ghasem A.
    Heidarkhani, Shapour
    [J]. DYNAMIC SYSTEMS AND APPLICATIONS, 2016, 25 (1-2): : 237 - 251
  • [46] INFINITELY MANY WEAK SOLUTIONS FOR A FOURTH-ORDER EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
    Tavani, Mohammad Reza Heidari
    Nazari, Abdollah
    [J]. MISKOLC MATHEMATICAL NOTES, 2019, 20 (01) : 525 - 538
  • [47] Infinitely many solutions to perturbed elliptic equations
    Schechter, M
    Zou, W
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 228 (01) : 1 - 38
  • [48] Multiple Solutions for Critical Fourth-Order Elliptic Equations of Kirchhoff type
    Fu Zhao
    Zeyi Liu
    Sihua Liang
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 1057 - 1064
  • [49] MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH MIXED NONLINEARITY
    Zhang, Wen
    Tang, Xianhua
    Zhang, Jian
    Luo, Zhiming
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017,
  • [50] EXISTENCE OF THREE NONTRIVIAL SOLUTIONS FOR A CLASS OF FOURTH-ORDER ELLIPTIC EQUATIONS
    Li, Chun
    Agarwal, Ravi P.
    Ou, Zeng-Qi
    [J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2018, 51 (02) : 331 - 344
12345