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Boundary Value Problems
Boundary Value Problems Cover Image
  • Research Article
  • Open Access

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

Boundary Value Problems20062007:014731

https://doi.org/10.1155/2007/14731

©  Tsing-San Hsu. 2007

  • Received: 19 July 2006
  • Accepted: 20 October 2006
  • Published:

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 .

Keywords

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

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Authors’ Affiliations

(1)
Center of General Education, Chang Gung University, Kwei-San, Tao-Yuan, 333, Taiwan

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Copyright

© Tsing-San Hsu. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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