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On the existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima

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Abstract

We study the problem of existence of periodic and almost periodic solutions of the scalar equation x′ (t) = − δx(t) + pmax u∈[t − h, t] x(u) + f(t) where δ, p ∈ R, with a periodic (almost periodic) perturbation f(t). For these solutions, we establish conditions of global exponential stability and prove uniqueness theorems.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. R. Bantsur

  2. Kiev Polytechnic Institute, Kiev

    O. P. Trofimchuk

Authors
  1. N. R. Bantsur
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  2. O. P. Trofimchuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 747–754, June, 1998.

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Bantsur, N.R., Trofimchuk, O.P. On the existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima. Ukr Math J 50, 847–856 (1998). https://doi.org/10.1007/BF02515218

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  • DOI: https://doi.org/10.1007/BF02515218

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