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Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity

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  • Alexandra Kashchenko

    (Centre of Integrable Systems, P. G. Demidov Yaroslavl State University, 150003 Yaroslavl, Russia)

Abstract

In this paper, we study nonlocal dynamics of a nonlinear delay differential equation. This equation with different types of nonlinearities appears in medical, physical, biological, and ecological applications. The type of nonlinearity in this paper is a generalization of two important for applications types of nonlinearities: piecewise constant and compactly supported functions. We study asymptotics of solutions under the condition that nonlinearity is multiplied by a large parameter. We construct all solutions of the equation with initial conditions from a wide subset of the phase space and find conditions on the parameters of equations for having periodic solutions.

Suggested Citation

  • Alexandra Kashchenko, 2022. "Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3360-:d:916448
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    References listed on IDEAS

    as
    1. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
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    Cited by:

    1. Alexandra Kashchenko & Sergey Kashchenko, 2023. "Relaxation Oscillations in the Logistic Equation with Delay and Modified Nonlinearity," Mathematics, MDPI, vol. 11(7), pages 1-18, April.

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