Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

Tsing-San Hsu

Abstract and Applied Analysis, 2007, vol. 2007, issue 1

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, u∈H01(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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https://doi.org/10.1155/2007/43018

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:043018

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