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).

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.

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.

scholarly journals Existence and Asymptotic Behavior of Positive Solutions of Functional Differential Equations of Delayed Type

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
J. Diblík ◽  
M. Kúdelčíková
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Positive Solutions ◽  
Linear Functional ◽  
Linear Equations ◽  
Functional Differential Equations ◽  
Right Hand ◽  
Functional Differential ◽  
The Right

Solutions of the equationy˙(t)= −f(t,yt)are considered fort→∞. The existence of two classes of positive solutions which are asymptotically different is proved using the retract method combined with Razumikhin's technique. With the aid of two auxiliary linear equations, which are constructed using upper and lower linear functional estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well.

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 Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann-Stieltjes Integrals

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.

scholarly journals Resolvent of nonautonomous linear delay functional differential equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Joël Blot ◽  
Mamadou I. Koné
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Differentiable Function ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Complete Proof ◽  
Right Hand ◽  
Linear Delay ◽  
Functional Differential ◽  
The Right

AbstractThe aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

scholarly journals On acyclicity of quadratic system with two non-rough foci

2021 ◽  
pp. 41-46
Author(s):  
Адам Дамирович Ушхо
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Phase Plane ◽  
Second Order ◽  
Quadratic System ◽  
Equilibrium States ◽  
System Of Differential Equations ◽  
Right Hand ◽  
The Right

Доказывается, что система дифференциальных уравнений, правые части которой представляют собой полиномы второй степени, не имеет предельных циклов, если в ограниченной части фазовой плоскости она имеет только два состояния равновесия и при этом они являются состояниями равновесия второй группы. It is proved that a system of differential equations, the right-hand sides of which are second-order polynomials, has no limit cycles if it has only two equilibrium states in the bounded part of the phase plane, and they are the equilibrium states of the second group.

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