Weak solution by the sub-supersolution method for a nonlocal system involving Lebesgue generalized spaces

Date

2022-05-01

Authors

Razani, Abdolrahman
Figueiredo, Giovany M.

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Publisher

Texas State University, Department of Mathematics

Abstract

We consider a system of nonlocal elliptic equations - A(x, |v|Lr1(x) div (α1(|∇u|p1(x))|∇u|p1(x)-2∇u) = ƒ1(x, u, v)|∇v|α1(x)Lq1(x) + g1(x, u, v)|∇v|γ1(x)Ls1(x), - A(x, |u|Lrs(x) div(αx(|∇v|p2(x))|∇u|p2(x)-2∇u) = ƒ2(x, u, v)|∇u|α2(x)Lq2(x) + g2(x, u, v)|∇u|γ2(x)Ls2(x), with Dirichlet boundary condition, where Ω is a bounded domain in ℝN (N > 1) with C2 boundary. Using sub-supersolution method, we provide the existence of at least one positive weak solution. Also, we study a generalized logistic equation and a sublinear system.

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Keywords

Nonlocal problem, p(x)-Laplacian, Sub-supersolution, Minimal wave speed

Citation

Razani, A., & Figueiredo, G. M. (2022). Weak solution by the sub-supersolution method for a nonlocal system involving Lebesgue generalized spaces. <i>Electronic Journal of Differential Equations, 2022</i>(36), pp. 1-18.

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Attribution 4.0 International

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