On the singular problem involving fractional g-Laplacian

Abstract

In this paper, we show the existence of weak a solution to the equation 0\\quad \\mbox{in}\\ \\Omega,\\\\ u & = 0\\quad \\mbox{in}\\ \\mathbb{R}^N\\setminus\\Omega \\end{split} \\end{align*} $$]]> ( − Δ g ) s u ( x ) = f ( x ) u ( x ) − q ( x ) in Ω , u > 0 in Ω , u = 0 in R N ∖ Ω where Ω is a smooth bounded domain in R N , q ∈ C 1 ( Ω ¯ ) , and ( − Δ g ) s is the fractional g-Laplacian with g is the antiderivative of a Young function and f in suitable Orlicz space. This includes the mixed fractional ( p , q ) − Laplacian as a special case. The solution so obtained is also shown to be locally Hölder continuous.