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Doklady Mathematics

, Volume 98, Issue 2, pp 425–429 | Cite as

Frequency Tests for the Existence and Stability of Bounded Solutions to Differential Equations of Higher Order

  • A. I. Perov
  • I. D. Kostrub
Mathematics

Abstract

To study a vector-matrix differential equation of order n, the method of integral equations is used. When the Lipschitz condition holds, an existence and uniqueness theorem for a bounded solution and its estimates are obtained. This solution is almost periodic if the nonlinearity is almost periodic, and it is asymptotically Lyapunov stable if the matrix characteristic polynomial is a Hurwitz polynomial. Under a Lipschitztype condition, a theorem on the existence of at least one bounded solution is proved; among the bounded solutions, there is at least one recurrent solution if the nonlinearity is almost periodic. The equation is S-dissipative if the matrix characteristic polynomial is a Hurwitz polynomial.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia

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