Open AccessStability of Positive Weak Solution for Generalized Weighted p-Fisher-Kolmogoroff Nonlinear Stationary-State Problem
Author(s) -
Salah A. Khafagy,
H. M. Serag
Publication year - 2022
Publication title -
european journal of mathematical analysis
Language(s) - English
Resource type - Journals
ISSN - 2733-3957
DOI - 10.28924/ada/ma.2.8
Subject(s) - bounded function , domain (mathematical analysis) , mathematics , laplace operator , combinatorics , p laplacian , function (biology) , state (computer science) , nonlinear system , stability (learning theory) , operator (biology) , boundary (topology) , mathematical analysis , physics , boundary value problem , chemistry , quantum mechanics , biochemistry , algorithm , repressor , evolutionary biology , machine learning , computer science , transcription factor , gene , biology
In the present paper, we investigate the stability results of positive weak solution for the generalized Fisher–Kolmogoroff nonlinear stationary-state problem involving weighted p-Laplacian operator −d∆P,pu = ka(x)u[ν − υu] in Ω, Bu = 0 on ∂Ω, where ∆P,p with p > 1 and P = P(x) is a weight function, denotes the weighted p-Laplacian defined by ∆P,pu ≡ div[P(x)|∇u|p−2∇u], the continuous function a(x): Ω → R satisfies either a(x) > 0 or a(x) < 0 for all x ∈ Ω, d, k, ν and υ are positive parameters and Ω ⊂ RN is a bounded domain with smooth boundary Bu = δh(x)u + (1 − δ) ∂u/∂n where δ ∈ [0, 1], h: ∂Ω → R+ with h = 1 when δ = 1.