Abstract
We construct uniform asymptotics of a solution of a heterogeneous system of singularly perturbed differential equations in the case of nondiagonalizable limit operator. We consider the case where the spectrum of the limit operator contains an unstable element at the point x = 0.
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References
Kh. L. Territin, “Asymptotic expansion of solutions of systems of ordinary differential equations with parameter,” Matematika, 1, No. 2, 29–59 (1957).
S. A. Lomov, Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).
N. I. Shkil’, I. I. Starun, and V. P. Yakovets, Asymptotic Integration of Linear Systems of Ordinary Differential Equations [in Russian], Vyshcha Shkola, Kiev (1989).
V. M. Bobochko and I. I. Markush, Asymptotic Integration of Differential Equations with Unstable Spectrum of Limit Operator [in Ukrainian], Vipol, Kiev (1993).
V. N. Bobochko, “Asymptotic integration of a system of differential equations with turning point,” Differents. Uravn., 27, No. 9, 1505–1515 (1991).
V. M. Bobochko, “Turning point in a system of differential equations with analytic operator,” Ukr. Mat. Zh., 48, No. 2, 147–160 (1996).
F. R. Gantmakher, Theory of Matrices [in Russian], Tekhteoretizdat, Moscow (1953).
N. M. Matveev, Methods for Integration of Ordinary Differential Equations [in Russian], Vysshaya Shkola, Moscow (1967).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 867–876, July, 1998.
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Bobochko, V.N. On the structure of solutions of a system of singularly perturbed differential equations with nondiagonalizable limit operator. Ukr Math J 50, 983–994 (1998). https://doi.org/10.1007/BF02528820
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DOI: https://doi.org/10.1007/BF02528820