Electron. J. Differential Equations, Vol. 2022 (2022), No. 36, pp. 1-18.

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

Abdolrahman Razani, Giovany M. Figueiredo

Abstract:
We consider a system of nonlocal elliptic equations

with Dirichlet boundary condition, where $\Omega$ is a bounded domain in $\mathbb{R}^N$ $(N >1)$ with $C^2$ boundary. Using sub-supersolution method, we prove the existence of at least one positive weak solution. Also, we study a generalized logistic equation and a sublinear system.

Submitted June 18, 2021. Published May 1, 2022
Math Subject Classifications: 35J91, 35J60, 35D30.
Key Words: Nonlocal problem, p(x)-Laplacian, sub-supersolution; minimal wave speed. DOI: https://doi.org/10.58997/ejde.2022.36

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Abdolrahman Razani
Department of Pure Mathematics
Faculty of Science
Imam Khomeini International University
Postal code: 34148-96818, Qazvin, Iran
email: razani@sci.ikiu.ac.ir
Giovany M. Figueiredo
Departamento de Matemática
Universidade de Brasilia
70.910-900, Brasilia (DF), Brazil
email: giovany@unb.br

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