scholarly journals Existence of Positive Solutions for a Class of Kirrchoff Elliptic Systems with Right Hand Side Defined as a Multiplication of Two Separate Functions

2021 ◽  
Vol 45 (4) ◽  
pp. 587-596
Author(s):  
YOUCEF BOUIZEM ◽  
◽  
, SALAH BOULAARAS ◽  
BACHIR DJEBBAR ◽  
◽  
...  
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Bounded Domains ◽  
Multiple Parameters ◽  
New Class ◽  
Right Hand ◽  
Existence Of Positive Solutions ◽  
The Right

The paper deals with the study of existence of weak positive solutions for a new class of Kirrchoff elliptic systems in bounded domains with multiple parameters, where the right hand side defined as a multiplication of two separate functions.

scholarly journals Existence of Positive Solutions for a Class of px,qx-Laplacian Elliptic Systems with Multiplication of Two Separate Functions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Youcef Bouizem ◽  
Salah Mahmoud Boulaaras ◽  
Ali Allahem
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Elliptic Systems ◽  
Subject Classification ◽  
New Class ◽  
Right Hand ◽  
Elliptic Differential Equations ◽  
Existence Of Positive Solutions ◽  
The Right

The paper deals with the study of the existence of weak positive solutions for a new class of the system of elliptic differential equations with respect to the symmetry conditions and the right hand side which has been defined as multiplication of two separate functions by using the sub-supersolutions method (1991 Mathematics Subject Classification: 35J60, 35B30, and 35B40).

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 of Kirchhoff hyperbolic systems with multiple parameters

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Mohamed Maizi ◽  
Salah Boulaaras ◽  
Abdelouahab Mansour ◽  
Mohamed Haiour
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Hyperbolic Systems ◽  
Bounded Domains ◽  
Multiple Parameters ◽  
Existence Of Positive Solutions

In this paper, by using sub-super solutions method, we study the existence of weak positive solution of Kirrchoff hyperbolic systems in bounded domains with multiple parameters. These results extend and improve many results in the literature

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.

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.

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