Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 537890, 18 pages
http://dx.doi.org/10.5402/2011/537890
Research Article

Asymptotic Periodicity for a Class of Partial Integrodifferential Equations

1Departamento de Matemática, Universidade Federal de Pernambuco, Recife 50540-740, PE, Brazil
2Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, Correo 2, Santiago, Chile

Received 1 March 2011; Accepted 27 April 2011

Academic Editor: M. S. Moslehian

Copyright © 2011 Alejandro Caicedo 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.

Linked References

  1. W. Desch, R. Grimmer, and W. Schappacher, “Well-posedness and wave propagation for a class of integrodifferential equations in Banach space,” Journal of Differential Equations, vol. 74, no. 2, pp. 391–411, 1988. View at Publisher · View at Google Scholar
  2. R. C. Grimmer, “Resolvent operators for integral equations in a Banach space,” Transactions of the American Mathematical Society, vol. 273, no. 1, pp. 333–349, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. R. Grimmer and J. Prüss, “On linear Volterra equations in Banach spaces,” Computers & Mathematics with Applications, vol. 11, no. 1–3, pp. 189–205, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. S. Aizicovici and M. McKibben, “Existence results for a class of abstract nonlocal Cauchy problems,” Nonlinear Analysis, vol. 39, no. 5, pp. 649–668, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. S. Aizicovici and H. Lee, “Nonlinear nonlocal Cauchy problems in Banach spaces,” Applied Mathematics Letters, vol. 18, no. 4, pp. 401–407, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. Liang, J. van Casteren, and T. J. Xiao, “Nonlocal Cauchy problems for semilinear evolution equations,” Nonlinear Analysis, vol. 50, no. 2, pp. 173–189, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. Hernández and J. P. C. dos Santos, “Asymptotically almost periodic and almost periodic solutions for a class of partial integro-differential equations,” Electronic Journal of Differential Equations, vol. 38, pp. 1–8, 2006. View at Google Scholar · View at Zentralblatt MATH
  8. H. S. Ding, T. J. Xiao, and J. Liang, “Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions,” Journal of Mathematical Analysis and Applications, vol. 338, no. 1, pp. 141–151, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. B. de Andrade and C. Cuevas, “S-asymptotically ω-periodic and asymptotically ω-periodic solutions to semilinear Cauchy problems with non dense domain,” Nonlinear Analysis, vol. 72, no. 6, pp. 3190–3208, 2010. View at Publisher · View at Google Scholar
  10. C. Cuevas, M. Pierri, and A. Sepulveda, “Weighted S-asymptotically ω-periodic solutions of a class of fractional differential equations,” Advances in Difference Equations, vol. 2011, Article ID 584874, 13 pages, 2011. View at Publisher · View at Google Scholar
  11. C. Cuevas and C. Lizama, “S-asymptotically ω-periodic solutions for semilinear Volterra equations,” Mathematical Methods in the Applied Sciences, vol. 33, no. 13, pp. 1628–1636, 2010. View at Google Scholar
  12. C. Cuevas and J. C. de Souza, “Existence of S-asymptotically ω-periodic solutions for fractional order functional integro-differential equations with infinite delay,” Nonlinear Analysis, vol. 72, no. 3-4, pp. 1683–1689, 2010. View at Publisher · View at Google Scholar
  13. C. Cuevas and J. C. de Souza, “S-asymptotically ω-periodic solutions of semilinear fractional integrodifferential equations,” Applied Mathematics Letters, vol. 22, no. 6, pp. 865–870, 2009. View at Publisher · View at Google Scholar
  14. H. R. Henríquez, M. Pierri, and P. Táboas, “On S-asymptotically ω-periodic functions on Banach spaces and applications,” Journal of Mathematical Analysis and Applications, vol. 343, no. 2, pp. 1119–1130, 2008. View at Publisher · View at Google Scholar
  15. H. R. Henríquez, M. Pierri, and P. Táboas, “Existence of S-asymptotically ω-periodic for abstract neutral equations,” Bulletin of the Australian Mathematical Society, vol. 78, no. 3, pp. 365–382, 2008. View at Publisher · View at Google Scholar
  16. S. Nicola and M. Pierri, “A note on S-asymptotically ω-periodic functions,” Nonlinear Analysis, vol. 10, no. 5, pp. 2937–2938, 2009. View at Publisher · View at Google Scholar
  17. C. Cuevas and H. R. Henríquez, “Solutions of second order abstract retarded functional differential equations on the line,” Journal of Nonlinear and Convex Analysis. In press.
  18. W. Desch, R. Grimmer, and W. Schappacher, “Some considerations for linear integro-differential equations,” Journal of Mathematical Analysis and Applications, vol. 104, no. 1, pp. 219–234, 1984. View at Publisher · View at Google Scholar
  19. A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, NY, USA, 2003.
  20. Y. Hino, S. Murakami, and T. Naito, Functional-Differential Equations with Infinite Delay, vol. 1473 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1991.
  21. B. D. Coleman and M. E. Gurtin, “Equipresence and constitutive equations for rigid heat conductors,” Zeitschrift fur Angewandte Mathematik und Physik, vol. 18, pp. 199–208, 1967. View at Google Scholar
  22. J. Liang and T. J. Xiao, “Semilinear integrodifferential equations with nonlocal initial conditions,” Computers & Mathematics with Applications, vol. 47, no. 6-7, pp. 863–875, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. R. K. Miller, “An integro-differential equation for rigid heat conductors with memory,” Journal of Mathematical Analysis and Applications, vol. 66, no. 2, pp. 313–332, 1978. View at Publisher · View at Google Scholar
  24. C. Chen, “Control and stabilization for the wave equation in a bounded domain,” SIAM Journal on Control and Optimization, vol. 17, no. 1, pp. 66–81, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. H. Brézis, Analyse Fonctionnelle, Masson, Paris, Farnce, 1993.