International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 73278, 26 pages
Existence and bifurcation for some elliptic problems on exterior
Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan
Received 21 December 2005; Revised 18 July 2006; Accepted 19 July 2006
Copyright © 2006 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 semilinear elliptic problem in , in , , where , , , and
is an exterior strip domain in . Under some suitable conditions on and , we show that there exists a positive constant such that the above semilinear elliptic problem has at least two solutions if , a unique
positive solution if , and no solution if
. We also obtain some bifurcation results of the solutions at .