Boundary Value Problems
Volume 2010 (2010), Article ID 524862, 21 pages
Research Article

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Department of Natural Sciences, Center for General Education, Chang Gung University, Tao-Yuan 333, Taiwan

Received 30 July 2010; Accepted 30 November 2010

Academic Editor: Wenming Z. Zou

Copyright © 2010 Tsing-San Hsu and Huei-Li Lin. 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.


Assume that 𝑞 is a positive continuous function in 𝑁 and satisfies the suitable conditions. We prove that the Dirichlet problem Δ 𝑢 + 𝑢 = 𝑞 ( 𝑧 ) | 𝑢 | 𝑝 2 𝑢 admits at least three positive solutions in an exterior domain.