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Mathematical Problems in Engineering
Volume 2006, Article ID 45468, 18 pages
http://dx.doi.org/10.1155/MPE/2006/45468

Null controllability of neutral evolution integrodifferential systems with infinite delay

Department of Mathematics, Bharathiar University, Coimbatore 641 046, India

Received 29 August 2004; Revised 30 May 2005; Accepted 26 March 2006

Copyright © 2006 K. Balachandran and A. Leelamani. 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. I. M. Ananjevskiĭ and V. B. Kolmanovskiĭ, “Stabilization of some nonlinear hereditary mechanical systems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 15, no. 2, pp. 101–114, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. K. Balachandran and E. R. Anandhi, “Neutral functional integrodifferential control systems in Banach spaces,” Kybernetika, vol. 39, no. 3, pp. 359–367, 2003. View at Google Scholar · View at MathSciNet
  3. K. Balachandran and J. P. Dauer, “Existence of solutions of a nonlinear mixed neutral equation,” Applied Mathematics Letters, vol. 11, no. 2, pp. 23–28, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  4. K. Balachandran and J. P. Dauer, “Controllability of nonlinear systems in Banach spaces: a survey,” Journal of Optimization Theory and Applications, vol. 115, no. 1, pp. 7–28, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. E. N. Chukwu, Differential Models and Neutral Systems for Controlling the Wealth of Nations, vol. 54 of Series on Advances in Mathematics for Applied Sciences, World Scientific, New Jersey, 2001. View at Zentralblatt MATH · View at MathSciNet
  6. C. Corduneanu and V. Lakshmikantham, “Equations with unbounded delay: a survey,” Nonlinear Analysis. Theory, Methods & Applications, vol. 4, no. 5, pp. 831–877, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  7. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. View at MathSciNet
  8. X. L. Fu, “Controllability of neutral functional differential systems in abstract space,” Applied Mathematics and Computation, vol. 141, no. 2-3, pp. 281–296, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. L. Fu, “Controllability of abstract neutral functional differential systems with unbounded delay,” Applied Mathematics and Computation, vol. 151, no. 2, pp. 299–314, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. L. Fu and K. Ezzinbi, “Existence of solutions for neutral functional differential evolution equations with nonlocal conditions,” Nonlinear Analysis, vol. 54, no. 2, pp. 215–227, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funkcialaj Ekvacioj, vol. 21, no. 1, pp. 11–41, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. R. Henríquez, “Periodic solutions of quasi-linear partial functional-differential equations with unbounded delay,” Funkcialaj Ekvacioj, vol. 37, no. 2, pp. 329–343, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. R. Henríquez, “Regularity of solutions of abstract retarded functional-differential equations with unbounded delay,” Nonlinear Analysis. Theory, Methods & Applications, vol. 28, no. 3, pp. 513–531, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. Hernández and H. R. Henríquez, “Existence results for partial neutral functional-differential equations with unbounded delay,” Journal of Mathematical Analysis and Applications, vol. 221, no. 2, pp. 452–475, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. Hino, S. Murakami, and T. Naito, Functional-Differential Equations with Infinite Delay, vol. 1473 of Lecture Notes in Mathematics, Springer, Berlin, 1991. View at Zentralblatt MATH · View at MathSciNet
  16. W. H. Kwon, G. W. Lee, and S. W. Kim, “Performance improvement using time delays in multivariable controller design,” International Journal of Control, vol. 52, no. 6, pp. 1455–1473, 1990. View at Google Scholar · View at Zentralblatt MATH
  17. B. N. Sadovskiĭ, “On a fixed point principle,” Functional Analysis and Applications, vol. 1, no. 2, pp. 74–76, 1967. View at Google Scholar · View at MathSciNet
  18. P. Sobolevskii, “On equations of parabolic type in Banach space,” American Mathematical Society Translations, vol. 49, pp. 1–62, 1965. View at Google Scholar