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

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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https://hal-upec-upem.archives-ouvertes.fr/hal-00693091
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Submitted on : Tuesday, May 1, 2012 - 8:06:47 PM
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  • HAL Id : hal-00693091, version 1

Citation

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, American Institute of Mathematical Sciences, 2007, 17 (4), pp.751--770. ⟨hal-00693091⟩

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