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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 631412, 19 pages
http://dx.doi.org/10.1155/2011/631412
Research Article

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.

Citations to this Article [8 citations]

The following is the list of published articles that have cited the current article.

  • Alexander Boichuk, Martina Langerová, and Jaroslava Škoríková, “Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems,” Abstract and Applied Analysis, vol. 2011, pp. 1–13, 2011. View at Publisher ยท View at Google Scholar
  • M. Medved', and M. Pospisil, “Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices,” Nonlinear Analysis-Theory Methods & Applications, vol. 75, no. 7, pp. 3348–3363, 2012. View at Publisher ยท View at Google Scholar
  • Josef Diblík, Denis Khusainov, Oleksandra Kukharenko, and Zdenek Svoboda, “Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay,” Abstract and Applied Analysis, vol. 2012, pp. 1–27, 2012. View at Publisher ยท View at Google Scholar
  • J. Diblík, M. Fečkan, and M. Pospíšil, “Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices,” Ukrainian Mathematical Journal, 2013. View at Publisher ยท View at Google Scholar
  • Josef Diblík, Michal Feckan, and Michal Pospíšil, “Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices,” Abstract and Applied Analysis, vol. 2013, pp. 1–10, 2013. View at Publisher ยท View at Google Scholar
  • O. A. Boichuk, and I. A. Golovats’ka, “Weakly Nonlinear Systems of Integrodifferential Equations,” Journal of Mathematical Sciences, 2014. View at Publisher ยท View at Google Scholar
  • M. Medved', M. Pospisil, and L. Skripkova, “On exponential stability of nonlinear fractional multidelay integro-differential equations defined by pairwise permutable matrices,” Applied Mathematics and Computation, vol. 227, pp. 456–468, 2014. View at Publisher ยท View at Google Scholar
  • Josef Diblík, and Blanka Morávková, “Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays,” Abstract and Applied Analysis, vol. 2014, pp. 1–19, 2014. View at Publisher ยท View at Google Scholar