Almost-periodic solutions of nonlinear impulse systems. (English. Russian original) Zbl 0693.34054
Ukr. Math. J. 41, No. 3, 259-263 (1989); translation from Ukr. Mat. Zh. 41, No. 3, 291-296 (1989).
On donne une définition nouvelle par rapport aux fonctions presque- périodiques et discontinues. On étudie des propriétés respectives. A la fin on trouve des solutions presque-périodiques des équations différentielles à impulsions.
Reviewer: S.Manolov
MSC:
| 34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 42A75 | Classical almost periodic functions, mean periodic functions |
Keywords:
differential equations with impulsesReferences:
| [1] | N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Fizmatgiz, Moscow (1963). |
| [2] | A. M. Samoilenko, N. A. Perestyuk, and M. U. Akhmetov, Almost Periodic Solutions of Differential Equations with Impulse Action [in Russian], Preprint 83.26, Math. Inst., Akad. Nauk Ukr. SSR (1983). · Zbl 0545.34030 |
| [3] | L. Amerio, ?Soluzioni quasi periodiche o limate, di sistemi differenziali non lineri quasi-periodici o limitati,? Ann. Math. Pura Appl.,39, 97-119 (1955). · Zbl 0066.07202 · doi:10.1007/BF02410765 |
| [4] | B. M. Levitan and V. V. Zhikov, Almost Periodic Functions and Differential Equations [in Russian], Moscow State Univ. (1978). · Zbl 0414.43008 |
| [5] | A. N. Kolmogorov, ?On the Skorokhod convergence,? Teor. Veroyatn. Primen.,1, No. 2, 239-247 (1956). · Zbl 0074.34102 |
| [6] | A. Halanay and D. Wexler, The Qualitative Theory of Systems with Impulse [in Rumanian], Editura Academiei Republicii Socialiste Romania, Bucuresti (1968) [Russian translation, Moscow, Mir (197l)]. · Zbl 0176.05202 |
| [7] | S. I. Gurgula and N. A. Perestyuk, ?Lyapunov’s second method in systems with impulse action,? Dokl. Akad. Nauk Ukr. SSR, Ser. A,10, 11-14 (1982). · Zbl 0502.34038 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
