Abstract

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.

Information

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

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