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Article

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

by
Alexandra Kashchenko
Centre of Integrable Systems, P. G. Demidov Yaroslavl State University, 150003 Yaroslavl, Russia
Mathematics 2022, 10(18), 3360; https://doi.org/10.3390/math10183360
Submission received: 29 July 2022 / Revised: 7 September 2022 / Accepted: 13 September 2022 / Published: 16 September 2022
(This article belongs to the Special Issue Advances in Delay Differential Equations)
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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.
Keywords: delay; asymptotics; large parameter; relaxation oscillations; periodic solutions delay; asymptotics; large parameter; relaxation oscillations; periodic solutions

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MDPI and ACS Style

Kashchenko, A. Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity. Mathematics 2022, 10, 3360. https://doi.org/10.3390/math10183360

AMA Style

Kashchenko A. Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity. Mathematics. 2022; 10(18):3360. https://doi.org/10.3390/math10183360

Chicago/Turabian Style

Kashchenko, Alexandra. 2022. "Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity" Mathematics 10, no. 18: 3360. https://doi.org/10.3390/math10183360

APA Style

Kashchenko, A. (2022). Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity. Mathematics, 10(18), 3360. https://doi.org/10.3390/math10183360

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