Overtaking Optimal Solutions for Convex Lagrange Problems with Time Delay

In this paper we study infinite horizon convex problems of Lagrange in which hereditary effects in the state are present. The objective functional in these problems is an improper integral defined over the time interval w0,q`.. Dictated by applications arising in mathematical economics we do not assume a priori that these improper integrals converge and therefore we consider overtaking optimal solutions. This concept arose in the economics literature in the 1960s. We extend known results for the analogous nondelay problem providing sufficient conditions for the existence of an overtaking optimal solution. Our proof rests on the assumption that a particular delay differential inclusion enjoys a strong asymptotic stability property called property S... Examples are given to indicate the applicability of these results.