Asymptotic behavior of bounded solutions for a system of neutral functional differential equations

Consider the system of neutral functional differential equations{(x1(t)−cx2(t−r))′=−F(x1(t))+G(x2(t−r)),(x2(t)−cx1(t−r))′=−F(x2(t))+G(x1(t−r)), where r>0r>0, c∈[0,1)c∈[0,1), F  , G∈C(R1)G∈C(R1) and F   is strictly increasing on R1R1. It is shown that if F(x)⩾G(x)F(x)⩾G(x) for all x∈R1x∈R1 or F(x)⩽G(x)F(x)⩽G(x) for all x∈R1x∈R1, then every bounded solution of such a system tends to an equilibrium. Our results improve and extend some corresponding ones already known.