abstract:In this paper, we study the existence of solution for the fourth-order three-point boundary value problem having the following formwhere η ∈ (0, 1), α, β ∈ R, f ∈ C([0, 1] × R, R), and f (t, 0) = 0. We give sufficient conditions that allow us to obtain the existence of solution. And by using the LeraySchauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.