Solutions for semilinear elliptic equations with critical exponents and Hardy potential

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• 作者：Cao ; Daomin ; Han ; Pigong
• 关键词：Semilinear elliptic equation ; Energy functional ; Palais&ndash ; Smale condition ; Critical Sobolev exponent
• 刊名：Journal of Differential Equations
• 出版年：2004
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：October 15, 2004
• 卷：205
• 期：2
• 页码：521-537
• 文件大小：273 K

摘要

In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let Ωs/glyphs/BQA.GIF>0 be an open-bounded domain, Ωs/glyphs/BOC.GIF>R^N(N≥5) and assume that 0≤μ<()²&minus;()², then, for all λ>0 there exists a nontrivial solution with critical level in the range (0,S<sub>μsub>) for the problem &minus;Δu&minus;μ=λu+|u|^2*&minus;2u in Ω; u=0 on ∂Ω.