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Existence Result for a Class of Nonlinear Elliptic Systems on Punctured Unbounded Domains

Abstract

We establish the existence of a nontrivial solution for systems with an arbitrary number of coupled Poisson equations with critical growth in punctured unbounded domains. The proof depends on a generalized linking theorem due to Krysewski and Szulkin, and on a concentration-compactness argument, proved by Frigon and the author. Applications to reaction-diffusion systems with skew gradient structure are also discussed in the last section.

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Correspondence to Fabrice Colin.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Colin, F. Existence Result for a Class of Nonlinear Elliptic Systems on Punctured Unbounded Domains. Bound Value Probl 2010, 175409 (2010). https://doi.org/10.1155/2010/175409

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Arbitrary Number
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