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On the Existence and Asymptotics of a Periodic Solution of a Degenerate Singularly Perturbed System of Differential Equations in the Case of Multiple Elementary Divisors

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Nonlinear Oscillations

Abstract

We consider a linear inhomogeneous singularly perturbed system of differential equations with ω-periodic coefficients and identically degenerate matrix with the derivative. We establish sufficient conditions for the existence and uniqueness of an ω-periodic solution of this system in the case where the main pencil of matrices has multiple spectrum. We construct asymptotics of this solution.

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Authors and Affiliations

  1. Gogol State Pedagogic University, Nizhyn

    V. P. Yakovets & A. M. Akymenko

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  1. V. P. Yakovets
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  2. A. M. Akymenko
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Yakovets, V.P., Akymenko, A.M. On the Existence and Asymptotics of a Periodic Solution of a Degenerate Singularly Perturbed System of Differential Equations in the Case of Multiple Elementary Divisors. Nonlinear Oscillations 5, 114–131 (2002). https://doi.org/10.1023/A:1014617314119

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  • DOI: https://doi.org/10.1023/A:1014617314119

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