Abstract and Applied Analysis

Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

Tsing-San Hsu

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 43018, 19 pages.

Dates
First available in Project Euclid: 23 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1174668659

Digital Object Identifier
doi:10.1155/2007/43018

Mathematical Reviews number (MathSciNet)
MR2283965

Zentralblatt MATH identifier
1157.35371

Citation

Hsu, Tsing-San. Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains. Abstr. Appl. Anal. 2007 (2007), Article ID 43018, 19 pages. doi:10.1155/2007/43018. https://projecteuclid.org/euclid.aaa/1174668659


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