In this paper we consider the following differential equation on a measure chain T u ∆∆ (t) + f (u(σ(t))) = 0, t ∈ [a, b] ∩ T, satisfying Sturm-Liouville boundary value conditions αu(a) − βu ∆ (a) = 0, γu(σ(b)) + δu ∆ (σ(b)) = 0. An existence result is obtained by using a Fixed Point Theorem due to Krasnoselskii and Zabreiko. Our conditions imposed on f are very easy to verify and our result is even new for the special cases of differential equations and difference equations, as well as in the general time scale setting.