Displaying similar documents to “Stability and periodicity for linear differential equations with periodic coefficients”

Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia

A. Halanay (2012)

Mathematical Modelling of Natural Phenomena

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Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem...

On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Jiří Šremr (2025)

Applications of Mathematics

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We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations....

Periodic solutions of a class of third-order differential equations with two delays depending on time and state

Rabah Khemis, Abdelouaheb Ardjouni, Ahlème Bouakkaz, Ahcene Djoudi (2019)

Commentationes Mathematicae Universitatis Carolinae

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The goal of the present paper is to establish some new results on the existence, uniqueness and stability of periodic solutions for a class of third order functional differential equations with state and time-varying delays. By Krasnoselskii's fixed point theorem, we prove the existence of periodic solutions and under certain sufficient conditions, the Banach contraction principle ensures the uniqueness of this solution. The results obtained in this paper are illustrated by an example. ...

Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces

Nguyen Thieu Huy, Ngo Quy Dang (2016)

Annales Polonici Mathematici

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We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence,...

Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

Bingwen Liu (2016)

Annales Polonici Mathematici

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This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.