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Minimal periods of periodic solutions of some Lipschitzian differential equations. (English) Zbl 1171.34343
Summary: A problem of finding lower bounds for periods of periodic solutions of a Lipschitzian differential equation, expressed in the supremum Lipschitz constant, is considered. Such known results are obtained for systems with inner product norms. However, utilizing the supremum norm requires development of a new technique, which is presented in this paper. Consequently, sharp bounds for equations of even order, both without delay and with arbitrary time-varying delay, are found. For both classes of system, the obtained bounds are attained in linear differential equations.
MSC:
34K13Periodic solutions of functional differential equations
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