Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators

Date

2007-05-09

Authors

Khafagy, Salah
Serag, Hassan M.

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Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

We study the maximum principle and existence of positive solutions for the nonlinear system -Δp,Pu = α(x)|u|p-2 u + b(x)|u|α|v|β v + ƒ in Ω, -ΔQ,qv = c(x)|u|α|v|β u + d(x)|v|q-2 v + g in Ω, u = v = 0 on ∂Ω, where the degenerate p-Laplacian defined as Δp,P u = div[P(x)|∇u|p-2∇u]. We give necessary and sufficient conditions for having the maximum principle for this system and then we prove the existence of positive solutions for the same system by using an approximation method.

Description

Keywords

Maximum principle, Existence of positive solution, Nonlinear elliptic system, Degenerated p-Laplacian

Citation

Khafagy, S. A., & Serag, H. M. (2007). Maximum principle and existence of positive solutions for nonlinear systems involving degenerate p-Laplacian operators. <i>Electronic Journal of Differential Equations, 2007</i>(66), pp. 1-14.

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Attribution 4.0 International

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