Construction of an asymptotic solution of the Cauchy problem for a degenerate linear system in the singular case. (English. Ukrainian original) Zbl 1276.34046
Nonlinear Oscil., N.Y. 11, No. 2, 286-304 (2008); translation from Nelinijni Kolyvannya 11, No. 2, 271-288 (2008).
Summary: We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for a singularly perturbed linear system of differential equations with degenerate matrix of coefficients of derivatives in the case when the limit pencil of matrices is singular.
MSC:
| 34E15 | Singular perturbations for ordinary differential equations |
| 34A30 | Linear ordinary differential equations and systems |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
References:
| [1] | F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1988). · Zbl 0666.15002 |
| [2] | N. I. Shkil’, I. I. Starun, and V. P. Yakovets’, Asymptotic Integration of Linear Systems of Differential Equations with Degeneracy [in Russian], Vyshcha Shkola, Kiev (1991). · Zbl 0743.34060 |
| [3] | A. M. Samoilenko, M. I. Shkil’, and V. P. Yakovets’, Linear Systems of Differential Equations with Degeneracy [in Ukrainian], Vyshcha Shkola, Kyiv (2000). |
| [4] | I. I. Starun, ”On the solution of the Cauchy problem for a singularly perturbed linear system,” Ukr. Mat. Zh., 43, No. 5, 715–718 (1991). · Zbl 0734.34050 |
| [5] | V. P. Yakovets’ and O. I. Kocherha, ”Asymptotics of a solution of the Cauchy problem for a degenerate singularly perturbed linear system in the case of a multiple spectrum of the main operator,” Dopov. Nats. Akad. Nauk Ukr., No. 5, 34–39 (1999). |
| [6] | O. I. Kocherha and V. P. Yakovets’, ”Asymptotic solution of the Cauchy problem for a degenerate singularly perturbed linear system in the case of a multiple spectrum of the main operator,” Nelin. Kolyvannya, 2, No. 1, 19–29 (1999). |
| [7] | O. I. Kocherga and V. P. Yakovets, ”The Cauchy problem for the degenerate singularly perturbed linear system in case of the multiple spectrum of the limit bundle of matrices,” Nonlin. Oscillations, 4, No. 2, 226–233 (2001). · Zbl 1049.34006 |
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