Oscillation of nonlinear elliptic inequalities with p(x)-Laplacian

2012 ◽  
Vol 58 (4) ◽  
pp. 537-546 ◽  
Author(s):  
Y. Şahiner ◽  
A. Zafer
Keyword(s):  
Nonlinear Elliptic ◽  
Elliptic Inequalities

Nonlinear elliptic inequalities with gradient terms on the Heisenberg group

2015 ◽  
Vol 121 ◽  
pp. 262-279 ◽  
Author(s):  
Sara Bordoni ◽  
Roberta Filippucci ◽  
Patrizia Pucci
Keyword(s):  
Heisenberg Group ◽  
Nonlinear Elliptic ◽  
Elliptic Inequalities

On a Nonlinear System of Reaction-Diffusion Equations

2006 ◽  
Vol 11 (2) ◽  
pp. 115-121 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Weak Solution ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic System ◽  
Positive Parameter ◽  
Nonlinear Elliptic ◽  
Positive Weak Solution

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system.

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