Sharkovsky-Type Theorems on S1 Applicable to Differential Equations
Abstract
“Period three implications” are investigated for a large class of multivalued maps on the circle. The obtained Sharkovsky–Block–Siegberg type theorem is then applied to differential equations and inclusions for the coexistence of infinitely many derivo–periodic solutions with various periods, sometimes called subharmonic solutions of the second kind. These deterministic results are also randomized. Several illustrative examples are supplied.