Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2009, Article ID 641368, 11 pages
http://dx.doi.org/10.1155/2009/641368
Research Article

Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

Department of Applied Mathematics, Donghua University, Shanghai 201620, China

Received 2 September 2009; Accepted 26 October 2009

Academic Editor: Guang Zhang

Copyright © 2009 Meili Li and Chunhai Kou. 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. D. D. Bainov and P. S. Simeonov, Systems with Impulse Effect, Stability, Theory and Applications, John Wiley & Sons, New York, NY, USA, 1989.
  2. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989. View at Zentralblatt MATH · View at MathSciNet
  3. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific, Singapore, 1995. View at MathSciNet
  4. X. Fu and Y. Cao, “Existence for neutral impulsive differential inclusions with nonlocal conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 12, pp. 3707–3718, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. Balachandran, J. Y. Park, and S. Marshal Anthoni, “Controllability of second order semilinear Volterra integrodifferential systems in Banach spaces,” Bulletin of the Korean Mathematical Society, vol. 36, no. 1, pp. 1–13, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Benchohra, J. Henderson, and S. K. Ntouyas, “Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 263, no. 2, pp. 763–780, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. R. Henríquez and M. Eduardo Hernández, “Approximate controllability of second-order distributed implicit functional systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 2, pp. 1023–1039, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Sakthivel, N. I. Mahmudov, and J. H. Kim, “On controllability of second order nonlinear impulsive differential systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 1-2, pp. 45–52, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C. C. Travis and G. F. Webb, “Cosine families and abstract nonlinear second order differential equations,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 32, no. 1-2, pp. 75–96, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. O. Fattorini, “Ordinary differential equations in linear topological spaces. I,” Journal of Differential Equations, vol. 5, pp. 72–105, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet