An Existence Result for a Class of Chemically Reacting Systems with Sign-Changing Weights
Year: 2015
Author: S. H. Rasouli, H. Norouzi
Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 1 : pp. 1–8
Abstract
We prove the existence of positive solutions for the system
{−Δpu=λa(x)f(v)u−α,x∈Ω,−Δqv=λb(x)g(u)v−β,x∈Ω,u=v=0,x∈∂Ω, where Δrz=div(|∇z|r−2∇z), for r>1 denotes the r-Laplacian operator and λ is a positive parameter, Ω is a bounded domain in Rn, n≥1 with sufficiently smooth boundary and α,β∈(0,1). Here a(x) and b(x) are C1 sign-changing
functions that maybe negative near the boundary and f,g are C1 nondecreasing functions, such that f,g: [0,∞)→[0,∞); f(s)>0, g(s)>0 for s>0, lims→∞g(s)=∞ and
lims→∞f(Mg(s)1q−1)sp−1+α=0,∀M>0.
We discuss the existence of positive weak solutions when f, g, a(x) and b(x) satisfy certain additional conditions. We employ the method of sub-supersolution to obtain our results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v28.n1.1
Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 1 : pp. 1–8
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Positive solutions
Author Details
S. H. Rasouli Email
H. Norouzi Email