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This article sets forth results on the existence, non-existence, uniqueness, and regularities properties, as well as boundary behavior of solutions for singular systems involving mixed local and non-local elliptic operators (see System (S) below). More precisely, we first establish a new weak comparison principle for a singular equation.
Afterward, we discuss the non-existence of positive classical solutions, as well as construct suitable ordered pairs of sub-solutions and super-solutions. This allows us to obtain the existence of a pair of positive weak solutions for System (S) by employing Schauder’s fixed-point theorem in the associated conical shell. Finally, we adapt a method of Krasnoselsky to establish the uniqueness of such a positive pair of
solutions.

Item Type	Journal
Divisions
ePrint ID	5249
Date Deposited	2024-12-17
Further Information	Google Scholar
URI	https://univ-soukahras.dz/en/publication/article/5249

@article{uniusa5249,
    title={A singular system involving mixed local and non-local operators},
    author={Abdelhamid Gouasmia},
    journal={Boundary Value Problems}
    year={2024},
    volume={2024},
    number={126},
    pages={},
    publisher={}
}