This paper studies the existence of solutions for a fourth order four-point boundary value problem on time scales. The results are obtained by an application of the Leray–Schauder fixed point theorem. This work is motivated by the continuous time results in [S. Chen, Wei Ni, C. Wang
, Appl. Math. Lett. 19, No. 2, 161–168 (2006; Zbl 1096.34009
)] for ordinary differential equations, and by the methods from [J.-P. Sun
, Nonlinear Anal., Theory Methods Appl. 64, No. 3 (A), 629–636 (2006; Zbl 1099.34022
)] for the third order problems on time scales.