The Brezis-Nirenberg Problem for the Henon Equation: Ground State Solutions

被引：0
|
作者：
Secchi, Simone [1 ]
机构：
[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy
来源：
ADVANCED NONLINEAR STUDIES | 2012年 / 12卷 / 02期
关键词：
Ground states; critical exponent; Henon equation; Nehari manifold; ASYMPTOTIC-BEHAVIOR; POSITIVE SOLUTIONS; PARTIAL SYMMETRY;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work is devoted to the Dirichlet problem for the equation -Delta u = lambda u + vertical bar x vertical bar(a)vertical bar u vertical bar(2 center dot-2) in the unit ball of R-N. We assume that lambda is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided alpha is small enough. This solution has a variational characterization as a ground state.
引用
收藏
页码：383 / 394
页数：12
相关论文
共 50 条
  • [1] EXISTENCE OF SOLUTIONS FOR THE BREZIS-NIRENBERG PROBLEM
    De Paiva, Francisco O.
    Miyagaki, Olimpio H.
    Presoto, Adilson E.
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2023, 61 (02) : 651 - 659
  • [2] MULTIPLE SOLUTIONS FOR THE BREZIS-NIRENBERG PROBLEM
    Clapp, Monica
    Weth, Tobias
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2005, 10 (04) : 463 - 480
  • [3] On the Brezis-Nirenberg Problem
    Schechter, M.
    Zou, Wenming
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 197 (01) : 337 - 356
  • [4] THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM
    Cao, Daomin
    Luo, Peng
    Peng, Shuangjie
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 374 (03) : 1947 - 1985
  • [5] SINGULAR SOLUTIONS OF THE BREZIS-NIRENBERG PROBLEM IN A BALL
    Flores, Isabel
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (02) : 673 - 682
  • [6] On the generalised Brezis-Nirenberg problem
    Anoop, T., V
    Das, Ujjal
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2023, 30 (01):
  • [7] The Brezis-Nirenberg problem on S
    Bandle, C
    Benguria, R
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 178 (01) : 264 - 279
  • [8] Multispike solutions for the Brezis-Nirenberg problem in dimension three
    Musso, Monica
    Salazar, Dora
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) : 6663 - 6709
  • [9] ON A BREZIS-NIRENBERG TYPE PROBLEM
    Catrina, Florin
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2006,
  • [10] ON THE BREZIS-NIRENBERG PROBLEM IN A BALL
    Chen, Zhijie
    Zou, Wenming
    DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (5-6) : 527 - 542
12345