PERIODIC-SOLUTIONS OF LINEAR INTEGRODIFFERENTIAL EQUATIONS

Using a degree‐theoretic result of Granas, a homotopy is constructed enabling us to show that if there is an a priori bound on all possible T‐periodic solutions of a Volterra equation, then there is a T‐periodic solution. The a priori bound is established by means of a Liapunov functional. The latter result is unusual in that no bounds on the Liapunov functional are required. Thus, in addition to the periodic solution, the equation may have both bounded and unbounded Solutions. Copyright © 1990 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim