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Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2007

Bubble tower solutions of slightly supercritical elliptic equations and application in symmetric domains

Yuxin Ge
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Ruihua Ang
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Feng Zhou

Abstract

We construct solutions of the semilinear elliptic problem {Delta u + \u\(p-1)u+epsilon(1)(2) f = 0 in Omega u = epsilon(1)(2) g on partial derivative Omega in a bounded smooth domain Omega subset of R-N ( N >= 3), when the exponent p is supercritical and close enough to N+2/N-2. As p --> N+2/N-2, the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves Green's function. As applications, we will give some existence results, in particular, when Omega are symmetric domains perforated with the small hole and when f = 0 and g = 0.
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Dates and versions

hal-00693091 , version 1 (01-05-2012)

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  • HAL Id : hal-00693091 , version 1

Cite

Yuxin Ge, Ruihua Ang, Feng Zhou. Bubble tower solutions of slightly supercritical elliptic equations and application in symmetric domains. Discrete and Continuous Dynamical Systems - Series S, 2007, 17 (4), pp.751--770. ⟨hal-00693091⟩
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