Krylov, Aleksandr Asymptotic integration of differential systems with internal resonances. (Russian. English summary) Zbl 0557.34003 Differ. Uravn. Primen. 35, 20-34 (1984). 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 Keywords:differential systems with internal resonance; perturbation method; resonance system PDFBibTeX XMLCite \textit{A. Krylov}, Differ. Uravn. Primen. 35, 20--34 (1984; Zbl 0557.34003)