Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth

被引：100
|
作者：
Cao, Daomin [2 ,3 ]
Peng, Shuangjie [1 ]
Yan, Shusen [4 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
[3] Chinese Acad Sci, Key Lab Random Complex Struct & Data Sci, Beijing 100190, Peoples R China
[4] Univ New England, Dept Math, Armidale, NSW 2351, Australia
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 06期
关键词：
Critical Sobolev growth; Infinitely many solutions; p-Laplacian equations; POSITIVE SOLUTIONS; EXISTENCE; MULTIPLICITY; TOPOLOGY; LINKING;
D O I：
10.1016/j.jfa.2012.01.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: -Delta(p)u = vertical bar u vertical bar(p)*(-2)u + mu vertical bar u vertical bar(p-2)u in Omega, u =0 on partial derivative Omega, provided N > p(2) + p, where Delta(p) is the p-Laplacian operator, 1 < p < N, p* = pN/N-p, mu > 0 and Omega is an open bounded domain in R-N. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：2861 / 2902
页数：42
相关论文
共 50 条
  • [1] Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent
    Wu, Yuanze
    Huang, Yisheng
    [J]. BOUNDARY VALUE PROBLEMS, 2013,
  • [2] Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent
    Yuanze Wu
    Yisheng Huang
    [J]. Boundary Value Problems, 2013
  • [3] Infinitely many solutions for a Hardy-Sobolev equation involving critical growth
    Peng, Shuangjie
    Wang, Chunhua
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (02) : 197 - 220
  • [4] Infinitely many solutions for a Dirichlet problem involving the p-Laplacian
    Bonanno, Gabriele
    Bisci, Giovanni Molica
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2010, 140 : 737 - 752
  • [5] Infinitely many solutions for the Dirichlet problem involving the p-Laplacian
    Cammaroto, F
    Chinnì, A
    Di Bella, B
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (1-2) : 41 - 49
  • [6] Remarks on the existence of infinitely many solutions for a p-Laplacian equation involving oscillatory nonlinearities
    Steglinski, Robert
    [J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2017, (56) : 1 - 12
  • [7] Infinitely many solutions via critical points for a fractional p-Laplacian equation with perturbations
    Keyu Zhang
    Donal O’Regan
    Jiafa Xu
    Zhengqing Fu
    [J]. Advances in Difference Equations, 2019
  • [8] Infinitely many solutions via critical points for a fractional p-Laplacian equation with perturbations
    Zhang, Keyu
    O'Regan, Donal
    Xu, Jiafa
    Fu, Zhengqing
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
  • [9] Infinitely Many Solutions for Mixed Elliptic Problems Involving the p-Laplacian
    Bonanno, Gabriele
    D'Agui, Giuseppina
    Papageorgiou, Nikolaos S.
    [J]. ADVANCED NONLINEAR STUDIES, 2015, 15 (04) : 939 - 950
  • [10] Infinitely Many Solutions for Critical Degenerate Kirchhoff Type Equations Involving the Fractional p-Laplacian
    Binlin, Zhang
    Fiscella, Alessio
    Liang, Sihua
    [J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2019, 80 (01): : 63 - 80
12345