Existence of bounded solutions of retarded functional differential equations (Q2729617)

The author deals with a system of retarded functional-differential equations NEWLINE\[NEWLINE\dot{y}(t)=f(t, y_t),NEWLINE\]NEWLINE where \(f: \Omega \rightarrow \mathbb{R}^n\) is continuous and satisfies a local Lipschitz condition with respect to the second argument, \(n\geq 2\) and \(\Omega \) is an open subset in \(\mathbb{R}\times K([-r, 0], \mathbb{R}^n)\). By developing a topological technique of \((n, p, z)\)-subsets, the existence of solutions to the above equation in an open domain is discussed. An application concerning the existence of bounded solutions to an equation of second order is given.