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Abstract and Applied Analysis
Volume 2007, Article ID 43018, 19 pages
Research Article

Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan

Received 7 July 2006; Revised 25 December 2006; Accepted 25 December 2006

Academic Editor: Martin J. Bohner

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 will show that under suitable conditions on f and h, there exists a positive number λ such that the nonhomogeneous elliptic equation Δu+u=λ(f(x,u)+h(x)) in Ω, uH01(Ω), N2, has at least two positive solutions if λ(0,λ), a unique positive solution if λ=λ, and no positive solution if λ>λ, where Ω is the entire space or an exterior domain or an unbounded cylinder domain or the complement in a strip domain of a bounded domain. We also obtain some properties of the set of solutions.