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.
Journal Title
Journal ISSN
Volume Title
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.
Rights
Attribution 4.0 International