Homoclinic solutions for a kind of neutral differential systems

Employing an extension of Mawhin’s continuation theorem and some analysis methods, we obtain the existence of homoclinic orbits for a type of neutral differential systems (u(t)−Cu(t−τ))′′+ddt∇F(u(t))+∇G(u(t))=e(t), where F∈C2(Rn,R)F∈C2(Rn,R); G∈C1(Rn,R);e∈C(R,Rn);C=diag(c1,c2,…,cn);ci and ττ are given constants, i=1,2,…,ni=1,2,…,n.