Abstract:
We survey the results relating to the theory of singular perturbations, in particular, to the theory of ordinary differential equations with a small parameter multiplying the highest derivative, that have been obtained by pupils of A. N. Tikhonov during the period 1966-1976. The main attention is directed at problems in which the roots of the characteristic equation have real parts of different signs (the conditionally stable case), and also at problems in which the characteristic equation has roots that are identically zero.
Citation:
A. B. Vasil'eva, “The development of the theory of ordinary differential equations with a small parameter multiplying the highest derivative during the period 1966–1976”, Russian Math. Surveys, 31:6 (1976), 109–131
\Bibitem{Vas76}
\by A.~B.~Vasil'eva
\paper The development of the theory of ordinary differential equations with a~small parameter multiplying the highest derivative during the period 1966--1976
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 6
\pages 109--131
\mathnet{http://mi.mathnet.ru/eng/rm4011}
\crossref{https://doi.org/10.1070/RM1976v031n06ABEH001580}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=473373}
\zmath{https://zbmath.org/?q=an:0366.34044|0376.34045}
Linking options:
https://www.mathnet.ru/eng/rm4011
https://doi.org/10.1070/RM1976v031n06ABEH001580
https://www.mathnet.ru/eng/rm/v31/i6/p102
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J. J. Mahony, J. J. Shepherd, “Stiff systems of ordinary differential equations. Part 1. Completely stiff, homogeneous systems”, J Aust Math Soc Series B Appl Math, 23:1 (1981), 17
R. E. O’Malley, Jr, “A Singular Singularly-Perturbed Linear Boundary Value Problem”, SIAM J Math Anal, 10:4 (1979), 695
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