Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2015, Article ID 456364, 8 pages
http://dx.doi.org/10.1155/2015/456364
Research Article

On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions

School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Received 7 March 2015; Revised 17 April 2015; Accepted 20 April 2015

Academic Editor: Jaume Giné

Copyright © 2015 Zhengxin Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Devlin, N. G. Lloyd, and J. M. Pearson, “Cubic systems and Abel equations,” Journal of Differential Equations, vol. 147, no. 2, pp. 435–454, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. L. A. Cherkas, “On the number of limit cycles of an autonomous second-order system,” Differential Equations, vol. 12, pp. 944–946, 1976. View at Google Scholar
  3. A. L. Neto, “On the number of solutions of the equations dx/dt  =j=0naj(t)xj, 0 t1; for which x0=x1,” Inventiones Mathematicae, vol. 59, pp. 67–76, 1980. View at Google Scholar
  4. Y. Lijun and T. Yuan, “Some new results on Abel equations,” Journal of Mathematical Analysis and Applications, vol. 261, no. 1, pp. 100–112, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. V. I. Mironenko, Analysis of Reflective Function and Multivariate Differential System, University Press, Gomel, Belarus, 2004.
  6. V. V. Mironenko, “Time-symmetry-preserving perturbations of differential systems,” Differential Equations, vol. 40, no. 10, pp. 1395–1403, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  7. V. I. Mironenko and V. V. Mironenko, “Time symmetries and in-period transformations,” Applied Mathematics Letters, vol. 24, no. 10, pp. 1721–1723, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. V. A. Bel’skii, “On the construction of first-order polynomial differential equations equivalent to a given equation in the sense of having the same reflective function,” Differential Equations, vol. 48, no. 1, pp. 13–20, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. V. A. Bel’skii and V. I. Mironenko, “Reflecting function preserving polynomial perturbations of Abel equation,” Problems of Physics, Mathematics and Technics, vol. 9, no. 4, pp. 79–85, 2011. View at Google Scholar
  10. V. A. Bel’skii and V. I. Mironenko, “Constructing of Abel equation equivalent to the equation of the form x=Atξ0+ξ1x+ξ2x2+ξ3x3,” Problems of Physics, Mathematics and Technics, vol. 11, no. 2, pp. 55–61, 2012. View at Google Scholar
  11. E. V. Musafirov, “Differential systems, the mapping over period for which is represented by a product of three exponential matrixes,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 647–654, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. V. Maiorovskaya, “Quadratic systems with a linear reflecting function,” Differential Equations, vol. 45, no. 2, pp. 271–273, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Z. X. Zhou, “On the Poincaré mapping and periodic solutions of nonautonomous differential systems,” Communications on Pure and Applied Analysis, vol. 6, no. 2, pp. 541–547, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus