Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

Tsing-San Hsu

Abstract and Applied Analysis, 2007, vol. 2007, 1-19

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:043018

DOI: 10.1155/2007/43018

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