An existence and uniqueness result for periodic solution of 2n-order differential equations

In this paper, we are concerned with the existence and uniqueness of solution to the 2n-order differential equation (-1)^n^-^1x^(^2^n^)+f(t,x,x^'^',...,x^2^(^n^-^1^))=0 with periodic boundary condition x^(^i^)(0)=x^(^i^)(2@p), i=0,1,...,2n-1. By using the initial value problem method, we transform the periodic boundary value problem into a problem of finding fixed point of continuous mapping.