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

摘要

In this paper, we are concerned with the existence and uniqueness of solution to the 2n-order differential equation (−1)n−1x(2n)+f(t,x,x′′,…,x2(n−1))=0 with periodic boundary condition x(i)(0)=x(i)(2π), 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.