Periodic Solution for Nonlinear Delay Equation in Higher Order

Abstract

In recent years, the existence and uniqueness of 2n-period solution for (1.1) [see pdf for notation] where x E Rn, and e(t,u,v) is a given function with 2^-period in t, have been discussed in several papers [1],[2],[3],[4] by using the Fourier expansion and fixed point method. The delay case is first discussed by W. Layton [5]. Applying similar ideas, we extend the study of (1.1) for any positive integer j.