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Sotnichenko, N. A.; Feshchenko, S. F.

An asymptotic solution for differential equations in a Banach space in the presence of a finite system of multiple eigenvalues. (English) Zbl 0354.34065

Ukr. Math. J. 28(1976), 506-512 (1977).
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MSC:

34G99 Differential equations in abstract spaces
34E05 Asymptotic expansions of solutions to ordinary differential equations
47A25 Spectral sets of linear operators
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References:

[1] S. F. Feshchenko, N. I. Shkil’, and L. D. Nikolenko, Asymptotic Methods in the Theory of Linear Differential Equatious [in Russian], Naukova Dumka, Kiev (1966).
[2] Yu. L. Daletskii, ?On certain equations with closed operators,? Izv. Kiev. Politekhn. In-ta,19, 157-177 (1956).
[3] T. Kato, Perturbation Theory of Linear Operators [in Russian], Mir, Moscow (1972). · Zbl 0247.47009
[4] M. M. Vainberg and V. A. Trenogin, Branching Theory for Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969). · Zbl 0274.47033
[5] N. I. Shkil’, ?On some asymptotic methods in the theory of linear differential equations with slowly varying coefficients,? Author’s Abstract of Doctoral Dissertation, Kiev.
[6] Yu. L. Daletskii and M. G. Krein, The Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).
[7] A. F. Turbin, ?A method of the theory of spectrally perturbed linear operators in asymptotic problems of the theory of probability,? Author’s Abstract of Candidate’s Dissertation, Kiev (1971).
[8] Ya. D. Plotkin and A. F. Turbin, ?The inversion of normally solvable linear operators,? Ukr. Mat. Zh.,27, No. 4, 477-487 (1975). · Zbl 0311.34076 · doi:10.1007/BF01089995
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