Periodic solutions of differential inclusions with retards

Abstract

The paper is devoted to study the existence of periodic solutions for retarded differential inclusions. The nonsmooth guiding potential method is used and topological degree theory for multivalued maps is applied.The present paper concerns the existence of periodic solutions for differential inclusions with retarded arguments of the form (Q F ) .

Periodic solutions for nonautonomous differential equations and inclusions in tubes

“…The methods have been mainly based on the degree theory (or fixed point index theory) applied to the single-valued or multivalued Poincaré operator of translation along trajectories. The guiding function method proposed by Krasnosel'skiȋ [10] has been successfully adopted for inclusions (1.1) (see, e.g., [7,9]) as well as for functional differential inclusions (see, e.g., [8] and the references therein). The main reason that we can use this method in a multivalued case is that the solution map very often has compact R δ values, so that its composition with the evaluation map is sufficiently good to apply the degree theory.…”