Abstract and Applied Analysis

Abstract and Applied Analysis / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 43018 | 19 pages | https://doi.org/10.1155/2007/43018

Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

Academic Editor: Martin J. Bohner
Received07 Jul 2006
Revised25 Dec 2006
Accepted25 Dec 2006
Published08 Feb 2007

Abstract

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.

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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.

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