In this paper, we show that if the Nemytskii operator maps the (p , α) -bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (p , α) -bounded variation space such that f (t , y) = g (t) y + h (t) for all t ∈ [ a , b ] , y ∈ ℝ .