- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 970469, 14 pages
Invariant Sets of Impulsive Differential Equations with Particularities in ω-Limit Set
Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Street 64, 01033 Kyiv, Ukraine
Received 19 January 2011; Accepted 14 February 2011
Academic Editor: Elena Braverman
Copyright © 2011 Mykola Perestyuk and Petro Feketa. 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.
- M. Akhmet, Principles of Discontinuous Dynamical Systems, Springer, New York, NY, USA, 2010.
- M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2 of Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, NY, USA, 2006.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Teaneck, NJ, USA, 1989.
- A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific, River Edge, NJ, USA, 1995.
- J. Moser, “On the theory of quasiperiodic motions,” SIAM Review, vol. 8, no. 2, pp. 145–172, 1966.
- N. Kryloff and N. Bogoliubov, Introduction to Non-Linear Mechanics, Annals of Mathematics Studies, no. 11, Princeton University Press, Princeton, NJ, USA, 1943.
- N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Non-Linear Oscillations, International Monographs on Advanced Mathematics and Physics, Gordon and Breach Science, New York, NY, USA, 1961.
- A. M. Samoĭlenko, Elements of the Mathematical Theory of Multi-Frequency Oscillations, vol. 71 of Mathematics and Its Applications (Soviet Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
- S. I. Dudzyaniĭ and M. O. Perestyuk, “On the stability of a trivial invariant torus of a class of systems with impulse perturbation,” Ukrainian Mathematical Journal, vol. 50, no. 3, pp. 338–349, 1998.
- M. O. Perestyuk and P. V. Feketa, “Invariant manifolds of a class of systems of differential equations with impulse perturbation,” Nonlinear Oscillations, vol. 13, no. 2, pp. 240–273, 2010.
- K. Schneider, S. I. Kostadinov, and G. T. Stamov, “Integral manifolds of impulsive differential equations defined on torus,” Proceedings of the Japan Academy, Series A, vol. 75, no. 4, pp. 53–57, 1999.
- V. I. Tkachenko, “The Green function and conditions for the existence of invariant sets of sampled-data systems,” Ukrainian Mathematical Journal, vol. 41, no. 10, pp. 1379–1383, 1989.
- M. O. Perestyuk and S. I. Baloga, “Existence of an invariant torus for a class of systems of differential equations,” Nonlinear Oscillations, vol. 11, no. 4, pp. 520–529, 2008.
- A. M. Samoilenko and N. A. Perestyuk, “On stability of the solutions of systems with impulsive perturbations,” Differential Equations, vol. 17, no. 11, pp. 1995–2001, 1981 (Russian).