Boundary Value Problems
Volume 2007 (2007), Article ID 14731, 25 pages
Eigenvalue Problems and Bifurcation of Nonhomogeneous Semilinear Elliptic Equations in Exterior
Center of General Education, Chang Gung University, Kwei-San, Tao-Yuan 333, Taiwan
Received 19 July 2006; Revised 10 October 2006; Accepted 20 October 2006
Academic Editor: Patrick J. Rabier
Copyright © 2007 Tsing-San Hsu. 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.
We consider the following eigenvalue problems: in in
where , , is a smooth bounded domain, , is a smooth bounded domain in
. 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 .