On the existence of positive solutions of some nonlocal elliptic problems involving fractional p–Laplacian operator

Abstract

Our aim in this paper is to analyze the existence of solutions to a nonlocal elliptic problem involving the fractional Laplacian operator. These operators are utilized to solve an equation defined within a bounded domain in . The operator is a fractional Laplacian , where with the condition and is a non-negative function almost everywhere with respect to the variable , and are real numbers. The article establishes two existence theorems for weak solutions using Tychonoff and Schauder fixed-point theorems. These theorems are formulated based on different hypotheses regarding the parameters and .