scholarly journals POSITIVE SOLUTION FOR A CLASS OF NONLOCAL ELLIPTIC SYSTEM WITH MULTIPLE PARAMETERS AND SINGULAR WEIGHTS

2017 ◽  
Vol 35 (1_2) ◽  
pp. 121-130
Author(s):  
G.A. AFROUZI ◽  
H. ZAHMATKESH
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Multiple Parameters ◽  
Singular Weights

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

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 ◽  
Existence Of Positive Solutions ◽  
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.

Existence of Nontrivial Positive Solutions to a Semilinear Elliptic System with Variable Coefficients

2012 ◽  
Vol 155-156 ◽  
pp. 678-681
Author(s):  
Da Wei Sun ◽  
Jia Rui Liu
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Variable Coefficients ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System

This paper studies the nontrivial positive solutions to a semilinear elliptic system with variable coefficients in the n dimensional Euclide space. By constructing a new variational space and using some linking theorems, this paper finally proves the existence of positive solution to a semilinear elliptic system.

Decaying positive solutions to a system of nonlinear elliptic equations

2006 ◽  
Vol 136 (2) ◽  
pp. 301-320
Author(s):  
Fenfei Chen ◽  
Miaoxin Yao
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Bounded Below

In this paper, the second-order nonlinear elliptic system with α, γ < 1 and β ≥ 1, is considered in RN, N ≥ 3. Under suitable hypotheses on functions fi, gi, hi (i = 1, 2) and P, it is shown that this system possesses an entire positive solution , 0 < θ < 1, such that both u and v are bounded below and above by constant multiples of |x|2−N for all |x| ≥ 1.

On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters

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 ◽  
Existence Of Positive Solutions ◽  
Bounded Smooth ◽  
Decreasing Functions

<p>We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form</p><span>{</span>Δu = α<sub>1</sub> (f (v)) - 1/<sub>u</sub><sup>n</sup>) + β<sub>1</sub>(h (u) - 1/<sub>u</sub><sup>n</sup>),     x € Ω),<br /> -Δv = α<sub>2</sub> (g (u)) - 1/<sub>v</sub><sup>θ</sup>) + β<sub>2</sub>(k (v) - 1/<sub>u</sub><sup>θ</sup>),    x € Ω), <br /> u = v = 0,                                                x € δΩ),<p>where Ω is a bounded smooth domain of R<sup>N</sup>, η, θ ε (0, 1), and α<sub>1</sub>, α<sub>2</sub>, β<sub>1</sub> and β<sub>2</sub> are nonnegative parameters. Here f, g, h, k ε C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) &gt; 0. We use the method of sub-super solutions to prove the existence of positive solution for α<sub>1</sub> + β<sub>1</sub> and α<sub>2</sub> + β<sub>2</sub> large.</p>

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

scholarly journals Symmetry and Nonexistence of Positive Solutions for a Fractional Laplacion System with Coupled Terms

2022 ◽  
Author(s):  
Rong Zhang
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Critical Case ◽  
Nonlinear Elliptic System ◽  
Subcritical Case ◽  
Nonlinear Elliptic ◽  
Method Of Moving Planes ◽  
Moving Planes

Abstract In this paper, we study the problem for a nonlinear elliptic system involving fractional Laplacion: (equation 1.1) where 0 < α, β < 2, p, q > 0 and max{p, q} ≥ 1, α + γ > 0, β + τ > 0, n ≥ 2. First of all, while in the subcritical case, i.e. n + α + γ − p(n − α) − (q + 1)(n − β) > 0, n + β + τ − (p + 1)(n − α) − q(n − β) > 0, we prove the nonexistence of positive solution for the above system in R n . Moreover, though Doubling Lemma to obtain the singularity estimates of the positive solution on bounded domain Ω. In addition, while in the critical case, i.e. n+α+γ −p(n−α)−(q + 1)(n−β) = 0, n+β +τ −(p+ 1)(n−α)−q(n−β) = 0, we show that the positive solution of above system are radical symmetric and decreasing about some point by using the method of Moving planes in Rn Mathematics Subject Classification (2020): 35R11, 35A10, 35B06.

Existence of Nontrivial Positive Solutions to a Semilinear Elliptic System

2012 ◽  
Vol 204-208 ◽  
pp. 4548-4551
Author(s):  
Da Wei Sun ◽  
Gao Sheng Zhu
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Embedding Theorems ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System

This paper studies the nontrivial positive solutions to a semilinear elliptic system in the n dimensional Euclide space. By constructing new variational space, using the linking theorems and some embedding theorems, this paper proves the existence of positive solution to a semilinear elliptic system, and improves the results of Li and Wang.

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