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2007 Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains
Tsing-San Hsu
Abstr. Appl. Anal. 2007: 1-19 (2007). DOI: 10.1155/2007/43018

Abstract

We will show that under suitable conditions on f and h , there exists a positive number λ such that the nonhomogeneous elliptic equation Δ u + u = λ ( f ( x , u ) + h ( x ) ) in Ω , u H 0 1 ( Ω ) , N 2 , 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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Tsing-San Hsu. "Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains." Abstr. Appl. Anal. 2007 1 - 19, 2007. https://doi.org/10.1155/2007/43018

Information

Published: 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1157.35371
MathSciNet: MR2283965
Digital Object Identifier: 10.1155/2007/43018

Rights: Copyright © 2007 Hindawi

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