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Warianty tytułu
Języki publikacji
Abstrakty
We give a few sufficient conditions for the existence of periodic solutions of the equation [formula] where n > r and aj 's, ck's are complex valued. We prove the existence of one up to two periodic solutions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
357--375
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Jagiellonian University Institute of Mathematics ul. Łojasiewicza 6, 30-348 Kraków, Poland, pawel.wilczynski@yahoo.pl
Bibliografia
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- [8] Y. Ilyashenko, Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions, Nonlinearity 13 (2000) 4, 1337–1342.
- [9] T. Kaczynski, R. Srzednicki, Periodic solutions of certain planar rational ordinary differential equations with periodic coefficients, Differential Integral Equations 7 (1994) 1, 37–47.
- [10] A. Lins Neto, On the number of solutions of the equation [formula].Invent. Math. 59 (1980) 1, 67–76.
- [11] N.G. Lloyd, The number of periodic solutions of the equation ż= zN + p1(t)zN-1 +: : : + pN(t), Proc. London Math. Soc. 27 (1973) 3, 667–700.
- [12] A.A. Panov, On the number of periodic solutions of polynomial differential equations, Mat. Zametki 64 (1998) 5, 720–727.
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- [14] V.A. Pliss, Nonlocal problems of the theory of oscillations, Translated from the Russian by Scripta Technica, Inc., Translation edited by Harry Herman, Academic Press, New York, 1966.
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- [16] J.H. Shapiro, Composition operators and classical function theory, [in:] Universitext:Tracts in Mathematics, Springer-Verlag, New York, 1993.
- [17] R. Srzednicki, On periodic solutions of planar polynomial differential equations with periodic coefficients, J. Differential Equations 114 (1994) 1, 77–100.
- [18] R. Srzednicki, Wazewski method and Conley index, [in:] Handbook of differential equations, Elsevier/North-Holland, Amsterdam, 2004, 591–684.
- [19] R. Srzednicki, K. Wójcik, A geometric method for detecting chaotic dynamics, J. Differential Equations 135 (1997) 1, 66–82.
- [20] R. Srzednicki, K. Wójcik, P. Zgliczynski, Fixed point results based on the Ważewski method, [in:] Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 905–943.
- [21] P. Wilczynski, Periodic solutions of polynomial planar nonautonomous equations, Ital. J. Pure Appl. Math. 21 (2007), 235–250.
- [22] P. Wilczynski, Planar nonautonomous polynomial equations: the Riccati equation, J. Differential Equations 244 (2008) 6, 1304–1328.
- [23] P. Wilczynski, Planar nonautonomous polynomial equations. II. Coinciding sectors, J. Differential Equations 246 (2009) 7, 2762–2787.
- [24] P. Wilczynski, Quaternionic-valued ordinary differential equations. The Riccati equation, J. Differential Equations 247 (2009) 7, 2163–2187.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0007-0026