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Asymptotic solutions to singularly perturbed differential equations with impulsive effects. (English) Zbl 1013.34055
Nikitin, A. G. (ed.), Group and analytic methods in mathematical physics. Kyïv: Instytut Matematyky NAN Ukraïny. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 36, 111-115 (2001).
The author considers the equation \(\varepsilon \frac{dx}{dt}=g(t,x)\) with a small parameter \(\varepsilon\) and impulsive conditions of the form \(\Delta x|_{t=t_i}=I_i(x)\) or \(\Delta x|_{t=t_i}=\varepsilon I_i(x)\) at an infinite sequence of points \(t_i\). Asymptotic series for solutions are found.
For the entire collection see [Zbl 0987.00013].
34E05 Asymptotic expansions of solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses