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Massera Problem for Some Nonautonomous Functional Differential Equations of Neutral Type with Finite Delay

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Abstract

The work considers the existence of periodic solutions for some nonautonomous nonlinear partial functional differential equations of neutral type with finite delay. It is supposed that the linear part is nondensely defined and satisfies the Acquistapace–Terreni conditions. The delayed part is assumed to be ω-periodic with respect to the first argument. The existence of periodic solutions is studied in the linear case by means of the existence of bounded solutions. In the nonlinear case, a fixed-point theorem for multivalued mapping and some sufficient conditions are given to prove the existence of periodic solutions. An example is given to illustrate the theoretical results.

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Authors and Affiliations

  1. Moulay Ismail University, Meknes, Morocco

    M. Es-saiydy, I. Oumadane & M. Zitane

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  1. M. Es-saiydy
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  2. I. Oumadane
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  3. M. Zitane
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Correspondence to M. Es-saiydy, I. Oumadane or M. Zitane.

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Translated by E. Oborin

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Es-saiydy, M., Oumadane, I. & Zitane, M. Massera Problem for Some Nonautonomous Functional Differential Equations of Neutral Type with Finite Delay. Russ Math. 66, 49–59 (2022). https://doi.org/10.3103/S1066369X22050036

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