A remark on the existence of positive weak solution for a class of -Laplacian nonlinear system with sign-changing weight

Rasouli, S. H.; Halimi, Z.; Mashhadban, Z.

doi:10.1016/j.na.2010.03.027

Cited by 14 publications

(5 citation statements)

References 18 publications

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“…Let (u 0 , v 0 ) be any positive weak solution of (1). We multiply the first and second equation of (1) by φ 1 , ψ 1 , respectively and integrate over Ω yields (26) −…”

Section: Stability and Instability Resultsmentioning

confidence: 99%

Existence and stability of positive weak solutions for a class of chemically reacting systems

2024

Eur. J. Math. Appl.

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In this article, we study the existence and nonexistence results of positive weak solutions for semilinear elliptic system of the form:where λ is a positive parameter, α,β ∈ (0, 1) and Ω ⊂ R n (n > 1) is a bounded domain with smooth boundary ∂Ω. Here f, g are C 1 non-decreasing functions such that f , g:) > 0 for u, v > 0 and a(x), b(x) are C 1 sign-changing functions that are probably negative near the boundary. In particular, on f (0, 0) or g(0, 0) there is no any sign conditions. Our approach is based on the sub-super solutions method. Also, under some certain conditions, we study the stability and instability properties of the positive weak solution for the system under consideration.

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“…Let (u 0 , v 0 ) be any positive weak solution of (1). We multiply the first and second equation of (1) by φ 1 , ψ 1 , respectively and integrate over Ω yields (26) −…”

Section: Stability and Instability Resultsmentioning

confidence: 99%

Existence and stability of positive weak solutions for a class of chemically reacting systems

2024

Eur. J. Math. Appl.

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“…This paper is motivated by results in [1][2][3][4][5]. We shall show the system (1) with signchanging weight functions has at least one solution.…”

Section: Contentmentioning

confidence: 97%

Sub-super solutions for (p-q) Laplacian systems

Haghaieghi

Afrouzi

2011

Bound Value Probl

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In this work, we consider the system: { - Δ p u = λ [ g ( x ) a ( u ) + f ( v ) ] in Ω - Δ q v = λ [ g ( x ) b ( v ) + h ( u ) ] in Ω u = v = 0 on ∂ Ω , where Ω is a bounded region in R N with smooth boundary ∂Ω, Δ p is the p-Laplacian operator defined by Δ p u = div (|∇u| p-2∇u), p, q > 1 and g (x) is a C 1 sign-changing the weight function, that maybe negative near the boundary. f, h, a, b are C 1 non-decreasing functions satisfying a(0) ≥ 0, b(0) ≥ 0. Using the method of sub-super solutions, we prove the existence of weak solution.

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“…If (p, q) = (2, 2), they are Newtonian fluids. One can refer to [5,14,17,22,23] for some existence results of (p, q)-Laplacian systems.…”

Section: Introductionmentioning

confidence: 99%

Extension of the Lotka-Volterra competition model

Rasouli

2024

Hacettepe Journal of Mathematics and Statistics

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A remark on the existence of positive weak solution for a class of -Laplacian nonlinear system with sign-changing weight

Cited by 14 publications

References 18 publications

Existence and stability of positive weak solutions for a class of chemically reacting systems

Existence and stability of positive weak solutions for a class of chemically reacting systems

Sub-super solutions for (p-q) Laplacian systems

Extension of the Lotka-Volterra competition model

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