Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

Tsing San Hsu; Huei Li Lin

doi:10.1017/S0308210509001462

Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

Tsing San Hsu^*
, Huei Li Lin

^*此作品的通信作者

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摘要

We study the existence and multiplicity of positive solutions for the Dirichlet problem -Δu=λf(z)|u| ^q-2u+|u| ^p-2u in Ω, where λ > 0, 1 < q < 2, p = 2* = 2N/(N - 2), 0 ∈ Ω ⊂ ℝ ^N, N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on Ω̄. Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.

原文	英語
頁（從 - 到）	115-135
頁數	21
期刊	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
卷	142
發行號	1
DOIs	https://doi.org/10.1017/S0308210509001462
出版狀態	已出版 - 02 2012

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AB - We study the existence and multiplicity of positive solutions for the Dirichlet problem -Δu=λf(z)|u| q-2u+|u| p-2u in Ω, where λ > 0, 1 < q < 2, p = 2* = 2N/(N - 2), 0 ∈ Ω ⊂ ℝ N, N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on Ω̄. Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.

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Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

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