Abstract: By using Fourier analysis and Leray-Schauder fixed point theorem, we discuss the existence and uniqueness of solutions of the fourth-order periodic boundary value problem. The existence and uniqueness of the solution of the problem are obtained under the condition that the nonlinear term f(x,u,v) satisfies an appropriate inequality.

Key words: fourth-order ordinary differential equation, Fourier analysis, Leray-Schauder fixed point theorem