Geodesic
On the periodic solutions of the rational differential equations
Problemy fiziki, matematiki i tehniki, no. 1 (2014), pp. 81-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2014},
     number = {1},
     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
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
%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