Weak Comparison Principle for Weighted Fractional p -Laplacian Equation

Abstract

The aim of this paper is to establish a weak comparison principle for a class fractional $p$ -Laplacian equation with weight. The nonlinear term $f\left(x,s\right)>0$ is a Carathéodory function which is possibly unbounded both at the origin and at infinity and such that $f\left(x,s\right)s^{1-p}$ decreases with respect to $s$ for a.e. $x\in \Omega$ .