Boundary Value Problems

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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: 27 December 2006

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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Authors’ Affiliations

(1)
Center of General Education, Chang Gung University

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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.