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Asymptotic integration of differential systems with internal resonances. (Russian. English summary) Zbl 0557.34003

Summary: The Cauchy problem for differential systems with internal resonance is considered. By means of the perturbation method the solution is uniformly valid when \(t\in [0;O(\epsilon^{-1})]\) is derived. The method can be used for a resonance system as well as for the nonresonance one. The problems of practical application of the present method are also discussed.

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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