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Journal of Applied Mathematics
Volume 2014, Article ID 419103, 10 pages
http://dx.doi.org/10.1155/2014/419103
Research Article

Pseudo Asymptotic Behavior of Mild Solution for Nonautonomous Integrodifferential Equations with Nondense Domain

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang 310023, China

Received 6 April 2014; Accepted 15 July 2014; Published 11 August 2014

Academic Editor: Bogdan Sasu

Copyright © 2014 Zhinan Xia. 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. N. S. Al-Islam, S. M. Alsulami, and T. Diagana, “Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6536–6548, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. Blot, G. M. Mophou, G. M. N'Guérékata, and D. Pennequin, “Weighted pseudo almost automorphic functions and applications to abstract differential equations,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 3-4, pp. 903–909, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. T. Diagana, “Weighted pseudo almost periodic functions and applications,” Comptes Rendus Mathematique, vol. 343, no. 10, pp. 643–646, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. C. Lizama and G. M. N'Guérékata, “Bounded mild solutions for semilinear integro differential equations in Banach spaces,” Integral Equations and Operator Theory, vol. 68, no. 2, pp. 207–227, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Z. Xia, “Weighted Stepanov-like pseudoperiodicity and applications,” Abstract and Applied Analysis, vol. 2014, Article ID 980869, 14 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. Blot, P. Cieutat, and K. Ezzinbi, “New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications,” Applicable Analysis, vol. 92, no. 3, pp. 493–526, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Blot, P. Cieutat, and K. Ezzinbi, “Measure theory and pseudo almost automorphic functions: new developments and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 4, pp. 2426–2447, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Abbas, “Pseudo almost automorphic solutions of some nonlinear integro-differential equations,” Computers and Mathematics with Applications, vol. 62, no. 5, pp. 2259–2272, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. H. S. Ding, J. Liang, and T. J. Xiao, “Pseudo almost periodic solutions to integro-differential equations of heat conduction in materials with memory,” Nonlinear Analysis: Real World Applications, vol. 13, no. 6, pp. 2659–2670, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. E. Hernández and J. P. C. Santos, “Asymptotically almost periodic and almost periodic solutions for a class of partial integrodifferential equations,” Electronic Journal of Differential Equations, vol. 2006, no. 38, pp. 1–8, 2006. View at Google Scholar
  11. C. Lizama and R. Ponce, “Bounded solutions to a class of semilinear integro-differential equations in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 10, pp. 3397–3406, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. I. Mishra and D. Bahuguna, “Weighted pseudo almost automorphic solution of an integro-differential equation, with weighted Stepanov-like pseudo almost automorphic forcing term,” Applied Mathematics and Computation, vol. 219, no. 10, pp. 5345–5355, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. Z. N. Xia, “Weighted pseudo almost automorphic solutions of hyperbolic semilinear integro-differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 95, pp. 50–65, 2014. View at Google Scholar
  14. T. Diagana, “Existence results for some nonautonomous integro-differential equations,” http://arxiv.org/abs/1402.5638v1.
  15. T. Diagana and G. M. N'Guérékata, “Pseudo almost periodic mild solutions to hyperbolic evolution equations in intermediate Banach spaces,” Applicable Analysis, vol. 85, no. 6-7, pp. 769–780, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  16. H. S. Ding, J. Liang, G. M. N'Guérékata, and T. J. Xiao, “Pseudo almost periodicity to some nonautonomous semilinear evolution equations,” Mathematical and Computer Modelling, vol. 45, pp. 579–584, 2007. View at Google Scholar
  17. K. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, vol. 194 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2000. View at MathSciNet
  18. A. M. Fink, Almost Periodic Differential Equations, Springer, New York, NY, USA, 1974. View at MathSciNet
  19. S. Bochner, “A new approach to almost periodicity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 48, pp. 2039–2043, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. C. Zhang, Pseudo almost periodic functions and their applications [Ph.D. thesis], University of Western Ontario, 1992.
  21. G. M. N'Guérékata, Topics in Almost Automorphy, Springer, New York, NY, USA, 2005.
  22. M. Adimy, K. Ezzinbi, and C. Marquet, “Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in fading memory spaces,” Journal of Applied Mathematics and Computing, vol. 44, no. 1-2, pp. 147–165, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. P. Acquistapace and B. Terreni, “A unified approach to abstract linear nonautonomous parabolic equations,” Rendiconti del Seminario Matematico della Università di Padova, vol. 78, pp. 47–107, 1987. View at Google Scholar · View at MathSciNet
  24. P. Acquistapace, “Evolution operators and strong solutions of abstract linear parabolic equations,” Differential and Integral Equations, vol. 1, no. 4, pp. 433–457, 1988. View at Google Scholar · View at MathSciNet
  25. Z. Hu and Z. Jin, “Almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 183420, 10 pages, 2013. View at Google Scholar · View at MathSciNet
  26. Z. R. Hu and Z. Jin, “Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 5-6, pp. 2349–2360, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. T. Diagana, “Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations,” Nonlinear Analysis, Theory, Methods and Applications, vol. 66, no. 2, pp. 384–395, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  28. G. M. N'Guérékata, “Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations,” Semigroup Forum, vol. 69, no. 1, pp. 80–86, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. T. Xiao, X. Zhu, and J. Liang, “Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications,” Nonlinear Analysis: Theory, Methods and Applications, vol. 70, no. 11, pp. 4079–4085, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, vol. 16 of Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, Basel, Switzerland, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  31. T. Diagana, “Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 69, no. 12, pp. 4277–4285, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. T. Diagana, “Existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 2, pp. 600–615, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. H. S. Ding, J. Liang, G. M. N'Guérékata, and T. Xiao, “Pseudo-almost periodicity of some nonautonomous evolution equations with delay,” Nonlinear Analysis: Theory, Methods and Applications, vol. 67, no. 5, pp. 1412–1418, 2007. View at Publisher · View at Google Scholar · View at Scopus