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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].
##### MSC:
 34E05 Asymptotic expansions of solutions to ordinary differential equations 34A37 Ordinary differential equations with impulses
##### Keywords:
impulsive conditions; asymptotic series