scholarly journals A remark on the existence of positive solutions for variable exponent elliptic systems

2013 ◽  
Vol 19 (1) ◽  
pp. 85-94
Author(s):  
G.A. Afrouzi ◽  
S. Shakeri ◽  
N.T. Chung
Keyword(s):  
Positive Solutions ◽  
Variable Exponent ◽  
Elliptic Systems ◽  
Existence Of Positive Solutions

Existence of Positive Solutions for a Class of Variable Exponent Elliptic Systems

2016 ◽  
Vol 118 (1) ◽  
pp. 83
Author(s):  
S. Ala ◽  
G. A. Afrouzi
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variable Exponent ◽  
Elliptic Systems ◽  
System Of Differential Equations ◽  
Existence Of Positive Solutions

We consider the system of differential equations \[ \begin{cases} -\Delta_{p(x)}u=\lambda^{p(x)}f(u,v)&\text{in $\Omega$,}\\ -\Delta_{q(x)}v=\mu^{q(x)}g(u,v)&\text{in $\Omega$,}\\ u=v=0&\text{on $\partial\Omega$,}\end{cases} \] where $\Omega \subset\mathsf{R}^{N}$ is a bounded domain with $C^{2}$ boundary $\partial \Omega,1<p(x),q(x)\in C^{1}(\bar{\Omega})$ are functions. $\Delta_{p(x)}u=\mathop{\rm div}\nolimits(|\nabla u|^{p(x)-2}\nabla u)$ is called $p(x)$-Laplacian. We discuss the existence of a positive solution via sub-super solutions.

Existence of positive solutions of a new class of nonlocal p⁢(x)p(x)-Kirchhoff parabolic systems via sub-super-solutions concept

2020 ◽  
Vol 26 (1) ◽  
pp. 49-58
Author(s):  
Sounia Zediri ◽  
Rafik Guefaifia ◽  
Salah Boulaaras
Keyword(s):  
Positive Solutions ◽  
Weak Solutions ◽  
Variable Exponent ◽  
Elliptic Systems ◽  
Parabolic Systems ◽  
Kirchhoff Type ◽  
Multiple Parameters ◽  
New Class ◽  
Existence Of Positive Solutions

AbstractMotivated by the idea which has been introduced by Boulaaras and Guefaifia [S. Boulaaras and R. Guefaifia, Existence of positive weak solutions for a class of Kirchhoff elliptic systems with multiple parameters, Math. Methods Appl. Sci. 41 2018, 13, 5203–5210] and by Afrouzi and Shakeri [G. A. Afrouzi, S. Shakeri and N. T. Chung, Existence of positive solutions for variable exponent elliptic systems with multiple parameters, Afr. Mat. 26 2015, 1–2, 159–168] combined with some properties of Kirchhoff-type operators, we prove the existence of positive solutions for a new class of nonlocal {p(x)}-Kirchhoff parabolic systems by using the sub- and super-solutions concept.

scholarly journals Existence of positive solutions for variable exponent elliptic systems

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Samira Ala ◽  
Ghasem Alizadeh Afrouzi ◽  
Qihu Zhang ◽  
Asadollah Niknam
Keyword(s):  
Positive Solutions ◽  
Variable Exponent ◽  
Elliptic Systems ◽  
Existence Of Positive Solutions

Positive solutions of certain elliptic systems with density-dependent diffusions

1995 ◽  
Vol 125 (5) ◽  
pp. 1031-1050 ◽  
Author(s):  
Inkyung Ahn ◽  
Lige Li
Keyword(s):  
Positive Solutions ◽  
Growth Rates ◽  
Smooth Boundary ◽  
Elliptic Systems ◽  
Biological Interactions ◽  
Bounded Region ◽  
Density Dependent ◽  
Existence Of Positive Solutions ◽  
Image Position ◽  
Increasing Functions

Results are obtained on the existence of positive solutions to the following elliptic system:in a bounded region Ω in Rn with a smooth boundary, where the diffusion terms φ ψ are non-negative functions and the system could be degenerate, β γ are strictly increasing functions, k,σ ≧ 0 are constants. We assume also that the growth rates f, g satisfy certain monotonicities. Applications to biological interactions with density-dependent diffusions are given.

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