Stability and periodicity for linear differential equations with periodic coefficients
L. Erbe (1975)
Annales Polonici Mathematici
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L. Erbe (1975)
Annales Polonici Mathematici
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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.
Božena Dorociaková, Rudolf Olach (2016)
Open Mathematics
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The paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.
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...
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,...
Dobrovol'skij, S.M., Rogozin, A.V. (2005)
Sibirskij Matematicheskij Zhurnal
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Olufemi Adeyinka Adesina (2001)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Lian, Jin-Guo (2009)
Applied Mathematics E-Notes [electronic only]
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A. T. ADEMOLA, M. O. OGUNDIRAN, P. O. ARAWOMO (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.