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An Existence Result for a Class of Chemically Reacting Systems with Sign-Changing Weights

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)uα,xΩ,Δqv=λb(x)g(u)vβ,xΩ,u=v=0,xΩ, where Δrz=div(|z|r2z), for r>1 denotes the r-Laplacian operator and λ is a positive parameter, Ω is a bounded domain in Rn, n1 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, limsg(s)= and

limsf(Mg(s)1q1)sp1+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