Solutions of Schrödinger equations with inverse square potential and critical nonlinearity
作者: Yinbin DengLingyu JinShuangjie Peng
作者单位: 1Department of Mathematics, Huazhong Normal University, Wuhan 430079, PR China
2College of Science, South China Agriculture University, Guangzhou 510642, PR China
刊名: Journal of Differential Equations, 2012, Vol.253 (5), pp.1376-1398
来源数据库: Elsevier Journal
DOI: 10.1016/j.jde.2012.05.009
关键词: CompactnessCritical Sobolev exponentNonlinear Schrödinger equationPositive solutionsPalais–Smale sequence
原始语种摘要: Abstract(#br)In this paper, we are concerned with the following nonlinear Schrödinger equations with inverse square potential and critical Sobolev exponent ( P ) − Δ u − μ u | x | 2 + a ( x ) u = | u | 2 ⁎ − 2 u + f ( x , u ) , u ∈ H 1 ( R N ) , where 2 ⁎ = 2 N / ( N − 2 ) is the critical Sobolev exponent, 0 ⩽ μ < μ ¯ : = ( N − 2 ) 2 4 , a ( x ) ∈ C ( R N ) . We first give a representation to the Palais–Smale sequence related to ( P ) and then obtain an existence result of positive solutions of ( P ) . Our assumptions on a ( x ) and f ( x , u ) are weaker than the known cases even if μ = 0 .
全文获取路径: Elsevier  (合作)
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来源刊物:
影响因子:1.48 (2012)

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关键词翻译
关键词翻译
  • exponent 指数
  • critical 临界的
  • dinger 铁道终点站站长
  • potential 
  • inverse 逆的
  • square 正方形
  • nonlinearity 非直线性
  • representation 表现
  • known 己知
  • sequence 次序