Abstract:
We develop an approach which we used to deduce conditions of a new type for the existence of periodic solutions of
ordinary differential equations and functional differential equations of point type. These conditions are based on
the use of asymptotic properties of solutions of differential equations which can be observed on shifts of solutions
and stated in terms of averages over the period on a distinguished sphere in the phase space. The development of
this approach enables us to obtain conditions for the existence of bounded solutions for the same classes of
functional differential equations.
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