On the periodic solutions of the rational differential equations
Problemy fiziki, matematiki i tehniki, no. 1 (2014), pp. 81-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper Mironenko method to study the periodic solutions of the rational differential equations is used. The obtained results to derive the sufficient conditions for a critical point of some polynomial differential systems to be a center are applied.
Keywords: reflecting function; center conditions; periodic solution.
@article{PFMT_2014_1_a13,
     author = {Zhengxin Zhou},
     title = {On the periodic solutions of the rational differential equations},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {81--84},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_1_a13/}
}
TY  - JOUR
AU  - Zhengxin Zhou
TI  - On the periodic solutions of the rational differential equations
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2014
SP  - 81
EP  - 84
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2014_1_a13/
LA  - en
ID  - PFMT_2014_1_a13
ER  - 
%0 Journal Article
%A Zhengxin Zhou
%T On the periodic solutions of the rational differential equations
%J Problemy fiziki, matematiki i tehniki
%D 2014
%P 81-84
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2014_1_a13/
%G en
%F PFMT_2014_1_a13
Zhengxin Zhou. On the periodic solutions of the rational differential equations. Problemy fiziki, matematiki i tehniki, no. 1 (2014), pp. 81-84. http://geodesic.mathdoc.fr/item/PFMT_2014_1_a13/

[1] M. A. M. Alwash, N. G. Lloyd, “Non-autonomous equations related to polynomial two-dimensional systems”, Proc. Roy. Soc. Edinburgh Sect. A, 105 (1987), 129–152 | DOI | MR | Zbl

[2] Yang Lijun, Tang Yuan, “Some new results on Abel equations”, J. Math. Anal. Appl., 261 (2001), 100–112 | DOI | MR | Zbl

[3] A. P. Sadowski, Polynomial ideals and manifold, University Press, Minsk, 2008

[4] V. I. Mironenko, Analysis of reflective function and multivariate differential system, University Press, Gomel, 2004, 196 pp. | Zbl

[5] V. I. Arnold, Ordinary differential equation, Science Press, M., 1971, 198–240

[6] V. I. Mironenko, “The reflecting function of a family of functions”, Differ. Equ., 36:12 (2000), 1636–1641 | DOI | MR | Zbl

[7] L. A. Alisevich, “On linear system with triangular reflective function”, Differ. Equ., 25:3 (1989), 1446–1449

[8] E. V. Musafirov, “Differential systems, the mapping over period for which is represented by a product of three exponential matrixes”, J. Math. Anal. Appl., 329 (2007), 647–654 | DOI | MR | Zbl

[9] V. V. Mironenko, “Time symmetry preserving perturbations of differential systems”, Differ. Equ., 40:20 (2004), 1395–1403 | DOI | MR | Zbl

[10] P. P. Verecovich, “Nonautonomous second order quadric system equivalent to linear system”, Differ. Equ., 34:12 (1998), 2257–2259

[11] S. V. Maiorovskaya, “Quadratic systems with a linear reflecting function”, Differ. Equ., 45:2 (2009), 271–273 | DOI | MR | Zbl

[12] Zhou Zhengxin, “On the reflective function of polynomial differential system”, J. Math. Anal. Appl., 278:1 (2003), 18–26 | DOI | MR | Zbl

[13] Zhou Zhengxin, “The structure of reflective function of polynomial differential systems”, Nonlinear Analysis, 71 (2009), 391–398 | DOI | MR | Zbl

[14] Zhou Zhengxin, “Research on the properties of some planar polynomial differential equations”, Appl. Math. Comput., 218 (2012), 5671–5681 | DOI | MR | Zbl