Periodic boundary-value problem for a fourth-order differential equation

In the present paper we obtain sufficient conditions for solvability of a periodic boundary-value problem for a fourth-order ordinary differential equation. The research technique is based on a solvability theorem for a quasi-linear operator equation in the resonance case. We formulate sufficient conditions for existence of periodic solutions in terms of the initial equation. The main result of the paper clarifies the existence theorem established by B. Mehry and D. Shadman in Sci. Iran. 15 (2), 182–185 (2008).