Abstract
In this chapter we provide a detailed discussion of the assumptions of the Tikhonov–Vasilyeva theory and give proofs of the main theorems.
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Braun, M.: Differential Equations and Their Applications. Springer, New York (1993)
Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer, Berlin 1991.
Hoppensteadt, F.C.: Stability with parameter. J. Math. Anal. Appl. 18, 129–134 (1967)
Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities, vol. 1. Academic, New York (1969)
O’Malley, R.E., Jr.: Singular Perturbation Methods for Ordinary Differential Equations. Springer, New York (1991)
Tikhonov, A.N.: On the dependence of the solutions of differential equations on a small parameters. Mat. Sbornik 22(64), 193–204 (1948 in Russian)
Tikhonov, A.N.: Systems of differential equations containing small parameters in the derivatives. Mat. Sbornik 31(73), 575–586 (1952 in Russian)
Tikhonov, A.N., Vasilyeva, A.B., Sveshnikov, A.G.: Differential Equations. Nauka, Moscow (1985 in Russian). English translation: Springer, Berlin (1985)
Vasilyeva, A.B.: Uniform approximations for the solutions of systems of differential equations with a small parameter. Mat. Sbornik 50, 43–58 (1960 in Russian)
Vasilyeva, A.B.: Asymptotic methods in the theory of ordinary differential equations with small parameters multiplying the highest derivatives. Uspehi Mat. Nauk 17, 225–231 (1962 in Russian)
Vasilyeva, A.B., Butuzov, V.F.: Asymptotic Expansions of Solutions of Singularly Perturbed Equations. Nauka, Moscow (1973 in Russian)
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Banasiak, J., Lachowicz, M. (2014). Tikhonov–Vasilyeva Theory. In: Methods of Small Parameter in Mathematical Biology. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05140-6_3
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DOI: https://doi.org/10.1007/978-3-319-05140-6_3
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Publisher Name: Birkhäuser, Cham
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