Melnikov functions and heteroclinic orbits in delay differential equations (Q757704)

The author gives sufficient conditions for the existence of bounded solutions for the perturbed delay differential equation \(\dot z(t)=g(z_ t)+h(t,z_ t,\epsilon)\) where \(h(t,\phi,0)=0\), \(\epsilon >0\), \(z_ t(\theta)=z(t+\theta)\), \(\theta\in [-r;0]\) with \(r>0\). The main tool is a theorem concerning the existence of an implicit solution for a functional equation. The method is based on the construction of ``Melnikov type functions''.