Abstract In this paper, we consider the following nonlinear elliptic equations involving the fractional p (x, ⋅) -Laplacian: (− Δ) p (x, ⋅) s u (x) = g (x, u (x), ∇ u (x) ), x ∈ Ω, u (x) > 0, x ∈ Ω, u (x) ≡ 0, x ∈ R N \ Ω, cases (-{) } (ₗ, ) ^su (x) =g (x, u (x), u (x) ), & x, \\ u (x) >0, & x, \\ u (x) 0, & x R^N, cases where Ω is a bounded or an unbounded domain, which is convex in x 1 -direction and the fractional p (x, ⋅) -Laplacian is defined by (− Δ) p (x
Wang et al. (2026) studied this question.