Multiplicity of Positive Solutions for Semilinear Elliptic Systems

Tsing-San Hsu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We study the effect of the coefficient h(x) of the critical nonlinearity on the number of positive solutions for semilinear elliptic systems. Under suitable assumptions for f(x), g(x), and h(x), we should prove that for sufficiently small λ, μ > 0, there are at least k + 1 positive solutions of the semilinear elliptic systems −Δu = λf(x) | u|q−2u + (α/(α + β))h(x) | u|α−2u | v|β, − Δv = μg(x) | v|q−2v + (β/(α + β))h(x) | u|α | v|β−2v, where 0 ∈ Ω ⊂ ℝN is a bounded domain, α > 1, β > 1, and N/(N − 2) 4.

Date: 2013
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https://doi.org/10.1155/2013/746380

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:746380

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