Existence and uniqueness of anti-periodic solutions for a class of nonlinear n-th order functional differential equations

In this paper, we use the method of coincide degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear $n$-th order functional differential equations of the form \begin{equation*} x^{(n)}(t)=F(t, x_t, x^{(n-1)}_t, x(t), x^{(n-1)}(t), x(t-au(t)), x^{(n-1)}(t-\sigma(t))).\end{equation*}