On the Existence of Positive Weak Solution for Nonlinear System with Singular Weights

Khafagy, S. A.; Serag, H. M.

doi:10.3103/s1068362320040068

Cited by 3 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, the existence of weak solutions for nonlinear elliptice systems involving p-Laplacian operators with different weights has been studied using an approximation method (see [25]), the theory of nonlinear monotone operators method (see [26]) and the sub-supersolutions method (see [10,11,14,19,20]). Recently, the behaviours and properties of the weak solution for some nonlinear systems have received considerable attention (see [1,[15][16][17][18])…”

Section: Introductionmentioning

confidence: 99%

Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type

2024

Eur. J. Math. Appl.

View full text Add to dashboard Cite

We establish the existence results of positive weak solution for the weighted p-Laplacian autocatalytic reaction problem −∆ P,p u = λm(x)[νa(x)u α − υu β ] in Ω, u = 0 on ∂Ω, where ∆ P,p with p > 1 and P = P (x) is a weight function, denotes the weighted p-Laplacian defined by ∆ P,p u ≡ div[P (x)|∇u| p−2 ∇u], m(x), a(x) are weight functions, λ, ν, υ are positive parameters, α + 1 ≤ p < β + 1, and Ω ⊂ R n is a bounded domain with smooth boundary ∂Ω. We establish that there exists positive constant λ * (Ω) such that the above system has a positive weak solution for λ ≥ λ * . We use the method of sub-supersolutions to establish our results.

show abstract

Section: Introductionmentioning

confidence: 99%

Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type

2024

Eur. J. Math. Appl.

View full text Add to dashboard Cite

show abstract

“…Many authors are interested in the study of existence results of weak solutions for linear [31], semilinear [15] and nonlinear systems [19]- [24] by using different methods. In [18,20], the subsuper solutions method is used to give necessary conditions for the existence of positive weak solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence results for fractional Fisher-Kolmogoroff steady state problem

2023

Eur. J. Math. Appl.

View full text Add to dashboard Cite

show abstract

Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

Serag¹,

Abdelrhman²,

Alsaban³

2021

APM

View full text Add to dashboard Cite

The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered.Finally, the problem for n × n cooperative elliptic systems under conjugation conditions is established.

show abstract

On the Existence of Positive Weak Solution for Nonlinear System with Singular Weights

Cited by 3 publications

References 12 publications

Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type

Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type

Existence results for fractional Fisher-Kolmogoroff steady state problem

Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

Contact Info

Product

Resources

About