Abstract:
Geometric methods of studying the problem of periodic solutions of differential inclusions are developed, and the notion of rotation of the vector field generated by a multivalued operator of parabolic type is introduced. Properties of the rotation are established, and applications to existence theorems for periodic solutions are given. Variants of the relationship principle are proved, as well as Bogolyubov's second theorem for operator differential inclusions. Possible applications are connected with the mechanics of viscoplastic media, extremal problems, and the theory of differential equations with deviating argument.
Bibliography: 19 titles.
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