Abstract
We investigate the solvability of the Cauchy problem for a linear singularly perturbed homogeneous system in the case of a singular pencil of matrices.
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REFERENCES
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1988).
N. I. Shkil', I. I. Starun, and V. P. Yakovets, Asymptotic Integration of Linear Systems of Differential Equations with Singularities [in Russian], Vyshcha Shkola, Kiev (1991).
I. I. Starun, “Construction of asymptotic solutions of singularly perturbed linear systems,” Differents. Uravn., 21, No. 10, 1822–1823 (1985).
I. I. Starun, “Construction of solutions for a class of linear systems,” in: Asymptotic Integration of Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985), pp. 153–160.
I. I. Starun, “Systems with a singular matrix at the derivative,” Ukr. Mat. Zh., 42, No. 1, 1535–1537 (1990).
I. I. Starun and M. I. Shkil', “Construction of solutions of linear and quasilinear singularly perturbed systems of ordinary differential equations,” in: Asymptotic Methods in Differential Equations [in Ukrainian], Vyshcha Shkola, Kiev (1993), pp. 141–157.
I. I. Starun and M. I. Shkil', “Integration of a singularly perturbed system with singularities,” Ukr. Mat. Zh., 47, No. 11, 1542–1548 (1995).
V. P. Yakovets, “Asymptotic analysis of a singularly perturbed linear system with a singular matrix pencil,” Ukr. Mat. Zh., 44, No. 1, 106–122 (1992).
A. M. Samoilenko, M. I. Shkil', and V. P. Yakovets, Linear Systems of Differential Equations with Singularities [in Ukrainian], Vyshcha Shkola, Kiev (2000).
G. S. Zhukova, A Method for a General Analysis of Linear Singularly Perturbed Differential Equations and Systems [in Russian], Autoref. Cand. Phys.-Math. Sci. Thesis, Moscow (1990).
N. I. Shkil', I. I. Starun, and V. P. Yakovets, Asymptotic Integration of Linear Systems of Differential Equations with Singularities [in Russian], Vyshcha Shkola, Kiev (1991).
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Starun, I.I., Shkil', M.I. Linear Singularly Perturbed Systems. Ukrainian Mathematical Journal 54, 2047–2054 (2002). https://doi.org/10.1023/A:1024033617266
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DOI: https://doi.org/10.1023/A:1024033617266