Homoclinic solutions for a class of neutral Duffing differential systems

By using an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic for a n-dimensional neutral Duffing differential systems, (u(t) - Cu(t - tau))'' + beta(t)x' (t) + g(u(t - gamma(t))) = p(t), is studied. Some new results on the existence of homoclinic solutions is obtained as a limit of a certain subsequence of the above set. Meanwhile, C = [C-ij](nxn) is a constant symmetrical matrix and beta(t) is allowed to change sign.