| Title:
|
On the ``Poincaré-Lyapunov”-like systems of three differential equations (English) |
| Title:
|
O systémech tří diferenciálních rovnic „Poincarého-Ljapunovova” typu (Czech) |
| Author:
|
Andres, Ján |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
25 |
| Issue:
|
1 |
| Year:
|
1986 |
| Pages:
|
165-180 |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34A34 |
| MSC:
|
34C15 |
| MSC:
|
34C25 |
| MSC:
|
34H05 |
| MSC:
|
93C15 |
| idZBL:
|
Zbl 0639.34041 |
| idMR:
|
MR918374 |
| . |
| Date available:
|
2009-01-29T15:32:07Z |
| Last updated:
|
2012-05-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120168 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/120223 |
| . |
| Reference:
|
[1] Poincaré H.: Sur les courbes définies par des équations differentielles.C. R. Acad. Sci. Paris, 94, 1882, 416-418. |
| Reference:
|
[2] Reissig R., Sansone G., Conti R.: Nichtlineare Differentialgleichungen höherer Ordnung.Cremonese, Roma, 1969. Zbl 0172.10801, MR 0241749 |
| Reference:
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[3] Krasovskii N. N.: On the stability of the solutions of a nonlinear system of three equations with any initial perturbations.(in Russian), Prikl. Mat. Mech., 17, 3, 1953, 339-350. MR 0055522 |
| Reference:
|
[4] Tuzov A. P.: Stability problems for a control system.(in Russian), Vestnik LGU, 10, 2, 1955, 43-70. MR 0069351 |
| Reference:
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[5] Tuzov A. P.: On the stability in the whole of a control system.(in Russian), Vestnik LGU, 12, 1, 1957, 57-75. |
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[6] Tuzov A. P.: On necessary and sufficient conditions for global stability of a control system.(in Russian), Dokl. Akad. Nauk SSSR, 4, 1960, 101-105. MR 0131631 |
| Reference:
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[7] Pliss V. A.: Investigation of a nonlinear system of three differential equations.(in Russian), Dokl. Akad. Nauk SSSR, 117, 1957, 184-187. Zbl 0127.04601, MR 0088616 |
| Reference:
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[8] Pliss V. A.: Necessary and sufficient conditions of stability in the whole for a system of three differential equations.(in Russian), Dokl. Akad. Nauk SSSR, 120, 1958, 708-710. MR 0114025 |
| Reference:
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[9] Pliss V. A.: On the Aizerman's problem in the case of a system of three differential equations.(in Russian), Dokl. Akad. Nauk SSSR, 121, 1958, 422-425. MR 0098228 |
| Reference:
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[10] Pliss V. A.: Some problems of stability of motion in the whole.(in Russian), Izdat. Leningrad. Univ., Leningrad, 1958. |
| Reference:
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[11] Pliss V. A.: Nonlocal problems of the theory of oscillations.(in Russian), Nauka, Moscow, 1964. MR 0171962 |
| Reference:
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[12] Reissig R.: Über die Stabilität eines Systems von autonomen Differentialgleichungen.Monatsber. Deutsch. Akad. Wiss., 7, 1965, 330-335. Zbl 0148.06902, MR 0188555 |
| Reference:
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[13] Reissig R.: Das Aisermansche Problem bei einem nichtlinearen System dritter Ordnung.Z. Angew. Math. Mech., 46, 1966, 79-82. MR 0221040 |
| Reference:
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[14] Reissig R.: Über die Stabilität eines Regelungssystems.Math.Nachr., 32, 1966, 63-72. Zbl 0143.11704, MR 0200547 |
| Reference:
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[15] Efendiev A. R., Balitinov M. A.: On the asymptotic stability in the whole of some nonlinear system.(in Russian), Diff. Urav., 4, 4, 1968. MR 0229923 |
| Reference:
|
[16] Balitinov M. A.: Behaviour of solutions in the large of a certain nonlinear system.(in Russian). Diff. Urav., 5, 1969, 254-262. |
| Reference:
|
[17] Balitinov M. A.: Certain theorems on the global behaviour of solutions of a certain nonlinear system.(in Russian), Ukrain. Mat. Zh., 23, 1971, 56-63. MR 0283317 |
| Reference:
|
[18] Gaishun I. V.: On the stability in the large of some optimal control system.(in Russian), Diff. Urav., 6, 5, 1970, 1953-1962. MR 0302267 |
| Reference:
|
[19] Gaishun I. V.: On the stability in the large of the motion defined by some nonlinear third order system.(in Russian), Diff. Urav., 5, 12, 1969. |
| Reference:
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[20] Barbashin E. A.: The Lyapunov functions.(in Russian), Nauka, Moscow, 1970. |
| Reference:
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[21] Egorov I. G.: The stability in the large of the zeгo solution of a certain system of three differential equations.(in Russian), Diff. Urav., 7, 1971, 1960-1966. MR 0289877 |
| Reference:
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[22] Zaprianov Z., Kalitzova P.: On the total stability of certain systems of differential equations of the third order.(in Russian), Theoret. Prilozh. Mech., 2, 1971, 2, 31-37, 4-5. MR 0298148 |
| Reference:
|
[23] Shiriaev V. I.: On the stability in the large of a third order system with "its own" nonlinearities in certain special case.(in Russian), Diff. Urav., 9, 1973, 2102-2104. MR 0330675 |
| Reference:
|
[24] Bihari I.: Perturbation theory of three-dimensional real linear autonomous systems.Studia Sci. Math. Hung., 1, 1966, 261-295. Zbl 0145.33703, MR 0206425 |
| Reference:
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[25] Bihari I., Elbert A.: Perturbation theory of three-dimensional real linear autonomous systems.Period. Math. Hung., 4. 4, 1973, 233-302. Zbl 0285.34036, MR 0350124 |
| Reference:
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[26] Schneider K. R.: Über die periodische Lösung eineг Klasse nicht-linearer autonomer Differentialgleichungssysteme dritter Ordnung.Z. Angew. Math. Mech., 49, 1969, 441-443. MR 0252763 |
| Reference:
|
[27] Schneider K. R.: Schranken für den Umfang und die Periode geschlossener Integralkurven von Differentialgleichungssystemen dritter und höherer Ordnung.Z. Angew. Math. Mech., 51, 1971, 149-151. Zbl 0219.34030, MR 0282002 |
| Reference:
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[28] Anitova E. S.: On the boudedness of solutions of a system of differential equations of the third order.(in Russian), Vestnik LGU, 19, 1, 1964, 5-14. MR 0165193 |
| Reference:
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[29] Anitova E. S.: On the boudedness of solutions of a system of differential equations of the third order.(in Russian), Vestnik LGU, 19, 7, 1964, 149-151. MR 0170074 |
| Reference:
|
[30] Villari G.: Soluzioni periodische di una classe di sistemi di tre equazioni differenziali ordinarie.Ann. Mat. Pura Appl., 4, 69, 1965, 191-200. MR 0190453 |
| Reference:
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[31] Müller W.: Hinreichende Bedingungen für die Beschränkheit der Lösungen eines Systems von drei Differentialgleichungen.Abh. Deutsch. Akad. Wiss., Kl. Math. Phys. Techn., 2, Akademie, Berlin, 1967. MR 0214881 |
| Reference:
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[32] Müller W.: Asymptotic behaviour of nonlinear systems of the third order.Proceed. Fourth. Conf. Nonlin. Oscill., Prague, 1967, Academia, Prague, 1968, 215-226. MR 0348207 |
| Reference:
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[33] Sansone G.: Nonlinear differential systems of the third and fourth order.Proceed. Conf. "Equadiff": Differential equations and their applications, Academia, Prague, 1963, 143-165. Zbl 0132.31803, MR 0168858 |
| Reference:
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[34] Andres J., Voráček J.: Periodic solutions of a certain parametric third order differential equation.Knižn. odb. vӗd. sp.VUT v Brně, B-94, 1983, 7-11. |
| Reference:
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[35] Andres J., Voráček J.: Periodic solutions to a nonlinear parametric differential equation of the third order.to appear in Rend. Accad. Naz. Lincei. 77, 3-4, Zbl 0607.34039, MR 0884940 |
| . |
