Existence of positive solutions of Kirchhoff hyperbolic systems with multiple parameters

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

On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters

Journal of the Indian Mathematical Society ◽

10.18311/jims/2017/6110 ◽

2017 ◽

Vol 84 (1-2) ◽

pp. 90

Author(s):

S. H. Rasouli

Keyword(s):

Nonlinear Systems ◽

Positive Solution ◽

Positive Solutions ◽

Smooth Domain ◽

Bounded Smooth Domain ◽

Multiple Parameters ◽

Bounded Smooth ◽

Decreasing Functions

We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form{Δu = α1 (f (v)) - 1/un) + β1(h (u) - 1/un), x € Ω), -Δv = α2 (g (u)) - 1/vθ) + β2(k (v) - 1/uθ), x € Ω), u = v = 0, x € δΩ),where Ω is a bounded smooth domain of RN, η, θ ε (0, 1), and α1, α2, β1 and β2 are nonnegative parameters. Here f, g, h, k ε C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α1 + β1 and α2 + β2 large.

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

Kragujevac Journal of Mathematics ◽

10.46793/kgjmat2104.587b ◽

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 ◽

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.

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2006.11.4.14736 ◽

2006 ◽

Vol 11 (4) ◽

pp. 323-329 ◽

Cited By ~ 1

Author(s):

G. A. Afrouzi ◽

S. H. Rasouli

Keyword(s):

Boundary Value Problems ◽

Positive Solution ◽

Bounded Domain ◽

Positive Solutions ◽

Elliptic Boundary ◽

Boundary Value ◽

Laplacian Operator ◽

Smooth Bounded Domain ◽

Elliptic Boundary Value ◽

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

ON EXISTENCE OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENCE EQUATIONS

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.25.1994.4453 ◽

1994 ◽

Vol 25 (3) ◽

pp. 257-265

Author(s):

J. H. SHEN ◽

Z. C. WANG ◽

X. Z. QIAN

Keyword(s):

Positive Integer ◽

Difference Equation ◽

Positive Solution ◽

Positive Solutions ◽

Difference Equations ◽

Real Numbers ◽

Neutral Difference Equation ◽

Neutral Difference Equations ◽

Consider the neutral difference equation \[\Delta(x_n- cx_{n-m})+p_nx_{n-k}=0, n\ge N\qquad (*) \] where $c$ and $p_n$ are real numbers, $k$ and $N$ are nonnegative integers, and $m$ is positive integer. We show that if \[\sum_{n=N}^\infty |p_n|<\infty \qquad (**) \] then Eq.(*) has a positive solution when $c \neq 1$. However, an interesting example is also given which shows that (**) does not imply that (*) has a positive solution when $c =1$.

The existence of positive solutions for an elliptic boundary value problem

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.2005 ◽

2005 ◽

Vol 2005 (13) ◽

pp. 2005-2010

Author(s):

G. A. Afrouzi

Keyword(s):

Boundary Conditions ◽

Positive Solution ◽

Positive Solutions ◽

Dirichlet Boundary ◽

Elliptic Boundary ◽

Dirichlet Boundary Conditions ◽

Mountain Pass Lemma ◽

First Eigenvalue ◽

Elliptic Boundary Value ◽

By using the mountain pass lemma, we study the existence of positive solutions for the equation−Δu(x)=λ(u|u|+u)(x)forx∈Ωtogether with Dirichlet boundary conditions and show that for everyλ<λ1, whereλ1is the first eigenvalue of−Δu=λuinΩwith the Dirichlet boundary conditions, the equation has a positive solution while no positive solution exists forλ≥λ1.

Existence of positive solutions of nonlocalp(x)-Kirchhoff hyperbolic systems via sub-super solutions concept

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-190884 ◽

2020 ◽

Vol 38 (4) ◽

pp. 4301-4313 ◽

Cited By ~ 3

Author(s):

Salah Boulaaras

Keyword(s):

Positive Solutions ◽

Hyperbolic Systems ◽

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

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-23298 ◽

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 ◽

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 Solution for a Singular Fourth–Order Differential System

Acta Marisiensis. Seria Technologica ◽

10.2478/amset-2021-0018 ◽

2021 ◽

Vol 18 (2) ◽

pp. 47-60

Author(s):

B. Kovács

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Positive Solution ◽

Positive Solutions ◽

Differential System ◽

Point Theorem ◽

Fourth Order ◽

Cone Expansion And Compression ◽

Compression Type

Abstract This paper investigates the existence of positive solutions for a fourth-order differential system using a fixed point theorem of cone expansion and compression type.

Existence of Positive Solutions of Nonlinear Second-Order M-Point Boundary Value Problem

International Journal of Artificial Life Research ◽

10.4018/jalr.2011010103 ◽

2011 ◽

Vol 2 (1) ◽

pp. 28-33

Author(s):

F. H. Wong ◽

C. J. Chyan ◽

S. W. Lin

Keyword(s):

Boundary Value Problem ◽

Positive Solution ◽

Positive Solutions ◽

Boundary Value ◽

Second Order ◽

Point Boundary ◽

Under suitable conditions on, the nonlinear second-order m-point boundary value problem has at least one positive solution. In this paper, the authors examine the positive solutions of nonlinear second-order m-point boundary value problem.

Existence results for a class of Kirchhoff type systems with Caffarelli-Kohn-Nirenberg exponents

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.1515/auom-2016-0004 ◽

2016 ◽

Vol 24 (1) ◽

pp. 83-94

Author(s):

G. A. Afrouzi ◽

H. Zahmatkesh ◽

S. Shakeri

Keyword(s):

Positive Solution ◽

Positive Solutions ◽

Type Systems ◽

Existence Results ◽

Kirchhoff Type ◽

Singular Weights

Abstract This paper is concerned with the existence of positive solutions for a class of infinite semipositone kirchhoff type systems with singular weights. Our aim is to establish the existence of positive solution for λ large enough. The arguments rely on the method of sub-and super-solutions.