International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 73278, 26 pages

Existence and bifurcation for some elliptic problems on exterior strip domains

Tsing-San Hsu

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 Δu+u=λK(x)up+f(x) in Ω, u>0 in Ω, uH01(Ω), where λ0, N3, 1<p<(N+2)/(N2), and Ω is an exterior strip domain in N. Under some suitable conditions on K(x) and f(x), we show that there exists a positive constant λ such that the above semilinear elliptic problem has at least two solutions if λ(0,λ), a unique positive solution if λ=λ, and no solution if λ>λ. We also obtain some bifurcation results of the solutions at λ=λ.