On the existence of positive solutions for an ecological model with indefinite weight | Zendy

S. Shakeri | Zendy; G. A. Afrouzi | Zendy; Armin Hadjian | Zendy

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On the existence of positive solutions for an ecological model with indefinite weight

Author(s) -

S. Shakeri,

G. A. Afrouzi,

Armin Hadjian

Publication year - 2015

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2014.12.002

Subject(s) - mathematics , bounded function , domain (mathematical analysis) , laplace operator , pure mathematics , weight function , mathematical analysis , boundary value problem , nonlinear system , function (biology) , p laplacian , boundary (topology) , physics , quantum mechanics , evolutionary biology , biology

This study concerns the existence of positive solutions for the following nonlinear boundary value problem: {−Δu=am(x)u−bu2−cupup+1−Kin Ω,u=0on ∂Ω, where Δu=div(∇u) is the Laplacian of u, while a,b,c,p,K are positive constants with p≥2 and Ω is a bounded smooth domain of RN with ∂Ω in C2. The weight function m satisfies m∈C(Ω) and m(x)≥m0>0 for x∈Ω, also ‖m‖∞=l<∞. We prove the existence of positive solutions under certain conditions

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