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Eigenvalue Problems and Bifurcation of Nonhomogeneous Semilinear Elliptic Equations in Exterior Strip Domains

Abstract

We consider the following eigenvalue problems: in in where,, is a smooth bounded domain,, is a smooth bounded domain in such that. Under some suitable conditions on and, we show that there exists a positive constant such that the above-mentioned problems have at least two solutions if, a unique positive solution if, and no solution if. We also obtain some bifurcation results of the solutions at.

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Correspondence to Tsing-San Hsu.

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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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Hsu, T. Eigenvalue Problems and Bifurcation of Nonhomogeneous Semilinear Elliptic Equations in Exterior Strip Domains. Bound Value Probl 2007, 014731 (2006). https://doi.org/10.1155/2007/14731

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Eigenvalue Problem