Перейти до основного вмісту
Construction of periodic solutions of degenerate singularly perturbed systems of differential equations with delayed argument
Samusenko Petro Fedorovych 1,2
1 Department of Theoretical Foundations of Informatics, National Pedagogical University named after M.P. Dragomanov, Kyiv, 011601, Ukraine
2 Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine "Igor Sicorsky Kyiv Polytechnic Institute", Kyiv, 03056, Ukraine
Keywords: degenerate singularly perturbed systems of differential equations
Abstract
We provide an algorithm for construction of periodic solution of degenerate singularly perturbed systems of differential equations with delay.
References

[1] Myshkis A.D. General theory of differential equations with a delayed argument // Uspekhi matematicheskikh nauk. - 1949. - 4, N5 (33). - P. 99-141.

[2] Vasilieva A.B., Rodionov A.M. Application of the perturbation method to an equation with a lagging argument in the case of a small lag // Proceedings of the seminar on the theory of differential equations with a deviating argument. - 1968. - 1. - P. 20-27.

[3] Ryabov Yu.A. The method of a small parameter in the theory of periodic solutions of differential equations with a delayed argument // Proceedings of the seminar on the theory of differential equations with a sloping argument. - 1962. -1. - P. 103-113.

[4] Kurdevanidze G.D. About the periodic mode of motion of a controlled object with a small delay. Automatic Control // Proceedings of the Institute of Systems and Control, Academy of Sciences of GSSR, Tbilisi. - 1974. - P. 168-181.

[5] Samoilenko A.M., Shkil M.I., Yakovets V.P. Linear systems of differential equations with degeneracy - K.: Higher School, 2000. - 294 p.

[6] Shkil N.I., Starun I.I., Yakovets V.P. Asymptotic integration of linear systems of ordinary differential equations. - K.:Vyshcha shk., 1989. - 287 p.

[7] Sibuya Y. Simplification of a system of linear ordinary differential equations about a singular point // Funkcialaj Ekvacioj. – 1962. – 4 . – P. 29-56.

[8] Samusenko P.F. Asymptotic integration of singularly perturbed systems of differential-functional equations with degeneracies - Kyiv: Drahomanov National Pedagogical University, 2011. 343 p.

[9] Kantorovich L.V., Akilov G.P. Functional Analysis. - M.: Nauka, 1977. - 744 p.

[10] Vasilieva A.B., Butuzov V.F. Singularly perturbed equations in critical cases. -M.: Izd-vo Mosk. univ., 1978. - 107 p.

Cite
ACS Style
Samusenko, P.F. Construction of periodic solutions of degenerate singularly perturbed systems of differential equations with delayed argument. Bukovinian Mathematical Journal. 2016, 1
AMA Style
Samusenko PF. Construction of periodic solutions of degenerate singularly perturbed systems of differential equations with delayed argument. Bukovinian Mathematical Journal. 2016; 1(3-4).
Chicago/Turabian Style
Petro Fedorovych Samusenko. 2016. "Construction of periodic solutions of degenerate singularly perturbed systems of differential equations with delayed argument". Bukovinian Mathematical Journal. 1 no. 3-4.
Export
We use own, third-party cookies, and localStorage files to analyze web traffic and page activities. Privacy Policy Settings