Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights
نویسندگان
چکیده
منابع مشابه
Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights
Recommended by Pavel Drabek We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu − μ/|x| 2 u λfx|u| q−2 u gx|u| 2 * −2 u in Ω, u 0 on ∂Ω, where 0 ∈ Ω ⊂ R N N ≥ 3 is a bounded domain with smooth boundary ∂Ω, λ > 0, 0 ≤ μ < μ N − 2 2 /4, 2 * 2N/N − 2, 1 ≤ q < 2, and f, g are continuous functions on Ω which are somewhere positive but which may change...
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Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 8 September 2010; Accepted 18 October 2010 Academic Editor: Julio Rossi Copyright q 2010 Tsing-San Hsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly c...
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and Applied Analysis 3 Theorem 1.1. Assume that (A1) and (B1) hold. If λ ∈ 0,Λ0 , then Eλa,b admits at least one positive solution inH1 R . Associated with Eλa,b , we consider the energy functional Jλa,b inH1 R : Jλa,b u 1 2 ‖u‖H1 − λ q ∫ RN a x |u|dx − 1 p ∫
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Let Ω 0 be an-open bounded domain in R N ≥ 3 and p∗ pN/ N − p . We consider the following quasilinear elliptic system of two equations inW 0 Ω ×W 1,p 0 Ω : −Δpu λf x |u|q−2u α/ α β h x |u|α−2u|v|β,−Δpv μg x |v|q−2v β/ α β h x |u|α|v|β−2v, where λ, μ > 0, Δp denotes the p-Laplacian operator, 1 ≤ q < p < N,α, β > 1 satisfy p < α β ≤ p∗, and f, g, h are continuous functions on Ω which are somewher...
متن کاملMultiple results for critical quasilinear elliptic systems involving concave-convex nonlinearities and sign-changing weight functions∗
This paper is devoted to study the multiplicity of nontrivial nonnegative or positive solutions to the following systems −4pu = λa1(x)|u|q−2u + b(x)Fu(u, v), in Ω, −4pv = λa2(x)|v|q−2v + b(x)Fv(u, v), in Ω, u = v = 0, on ∂Ω, where Ω ⊂ R is a bounded domain with smooth boundary ∂Ω; 1 < q < p < N , p∗ = Np N−p ; 4pw = div(|∇w|p−2∇w) denotes the p-Laplacian operator; λ > 0 is a positive pa...
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ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2009
ISSN: 1687-2762,1687-2770
DOI: 10.1155/2009/584203