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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 631412, 19 pages
Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems
1Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya Street 3, 01601 Kyiv, Ukraine
2Department of Mathematics, University of Žilina, Univerzitná 8215/1, 01026 Žilina, Slovakia
3Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech Republic
4Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 10, 616 00 Brno, Czech Republic
5Department of Complex System Modeling, Faculty of Cybernetics, Taras, Shevchenko National University of Kyiv, Vladimirskaya Street 64, 01033 Kyiv, Ukraine
Received 30 January 2011; Accepted 31 March 2011
Academic Editor: Elena Braverman
Copyright © 2011 A. Boichuk et al. 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.
- N. V. Azbelev and V. P. Maksimov, “Equations with delayed arguments,” Differential Equations, vol. 18, pp. 1419–1441, 1983, translated in Differentsial'nye Uravneniya, Vol. 18, no. 12, pp. 2027-2050.
- A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary Value Problems, VSP, Boston, Mass, USA, 2004.
- J. Hale, Theory of Functional Differential Equations, Applied Mathematical Sciences, Vol. 3, Springer, New York, NY, USA, 2nd edition, 1977.
- J. Mallet-Paret, “The fredholm alternative for functional-differential equations of mixed type,” Journal of Dynamics and Differential Equations, vol. 11, no. 1, pp. 1–47, 1999.
- D. Ya. Khusainov and G. V. Shuklin, “Relative controllability in systems with pure delay,” International Applied Mechanics, vol. 41, no. 2, pp. 210–221, 2005, translated in Prikladnaya Mekhanika, Vol. 41, no. 2, pp. 118-130.
- A. A. Boichuk, J. Diblík, D. Khusainov, and M. Růžičková, “Fredholm's boundary-value problems for differential systems with a single delay,” Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 5, pp. 2251–2258, 2010.
- A. A. Boichuk, J. Diblík, D. Y. A. Khusainov, and M. Růžičková, “Boundary value problems for delay differential systems,” Advances in Difference Equations, vol. 2010, Article ID 593834, 10 pages, 2010.
- M. Medvĕd, M. Pospíšil, and L. Škripková, “Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts defined by permutable matrices,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 12, pp. 3903–3911, 2011.
- A. A. Boichuk and M. K. Grammatikopoulos, “Perturbed fredholm boundary value problems for delay differential systems,” Abstract and Applied Analysis, no. 15, pp. 843–864, 2003.
- A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, “Generalized inverse operators and noether boundary-value problems,” in Proceedings of the Institute of Mathematics of the National Academy of Sciences of the Ukraine, vol. 13, p. 320, Kyiv, Ukrania, 1995.
- I. G. Malkin, Some Problems in the Theory of Nonlinear Oscillations, Gostekhizdat, Moscow, Russia, 1956.
- M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Y. A. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations, Nauka, Moscow, Russia, 1968, Translation: Noordhoff, Groningen, 1972.