On some properties of degenerate linear systems
Article
Received:
- 24 Downloads
- 6 Citations
Abstract
For a linear system of ordinary differential equations with degenerate matrix of derivatives, we find conditions of reducibility to the central canonical form. We also establish the structure of the general solution and conditions of solvability of the Cauchy problem, and study the problem of periodic solutions.
Keywords
Periodic Solution Cauchy Problem Homogeneous System Singular System Fundamental Matrice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Yu. E. Boyarintsev, Regular and Singular Systems of Linear Ordinary Differential Equations [in Russian], Nauka, Novosibirsk (1980).MATHGoogle Scholar
- 2.Yu. E. Boyarintsev, V. A. Danilov, A. L. Loginov, and V. F. Chistyakov, Numerical Methods for the Solution of Singular Systems [in Russian], Nauka, Novosibirsk (1989).MATHGoogle Scholar
- 3.V. F. Chistyakov, “On singular systems of ordinary differential equations and their integral analogs”, in: Lyapunov Functions and Their Application [in Russian], Nauka, Novosibirsk (1985), pp. 231–240.Google Scholar
- 4.Yu. D. Shlapak, “Periodic solutions of a linear system of differential equations with a degenerate matrix with a derivative,” Ukr. Mat. Zh., 27, No. 1, 137–140 (1975).MATHCrossRefGoogle Scholar
- 5.V. A. Eremenko, “On the reduction of a linear system of differential equations with a degenerate matrix with derivatives,” Ukr. Mat. Zh., 32, No. 2, 168–174 (1980).MATHCrossRefMathSciNetGoogle Scholar
- 6.S. L. Campbell, Singular System of Differential Equations. I, Pitman (1982).Google Scholar
- 7.S. L. Campbell, Singular System of Differential Equations. II, Pitman (1982).Google Scholar
- 8.S. L. Campbell and L. R. Petzold, “Canonical forms and solvable singular systems of differential equations,” SIAM J. Ald. Discrete Methods, No. 4, 517–521 (1983).CrossRefMathSciNetGoogle Scholar
- 9.S. L. Campbell, “A general form and solvable linear time varying singular systems of differential equations,” SIAM J. Math. Anal., 18, No. 4, 1101–1115 (1987).MATHCrossRefMathSciNetGoogle Scholar
- 10.Y. Sibuya, “Some global properties of functions of one variable,” Math. Ann., 161, No. 1, 67–77 (1965).MATHCrossRefMathSciNetGoogle Scholar
- 11.S. L. Campbell and C. D. Meyer, jr., Generalized Inverses of Linear Transformations, Pitman (1979).Google Scholar
- 12.A. M. Samoilenko and V. P. Yakovets, “On the reducibility of a degenerate linear system to the central canonical form,” Dopov. Akad. Nauk Ukr., No. 4, 10–15 (1993).MathSciNetGoogle Scholar
- 13.A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Moscow, Nauka (1987).Google Scholar
Copyright information
© Plenum Publishing Corporation 1998