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Weighted pseudo almost periodic solutions for a class of discrete hematopoiesis model

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Abstract

In this paper, we first investigate some basic and essential properties of weighted pseudo almost periodic sequences. Then we discuss the existence of weighted pseudo almost periodic solutions for a class of discrete hematopoiesis model.

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References

  1. Diagana, T.: Weighted pseudo almost periodic functions and applications. C. R. Acad. Sci. Paris, Ser. I. 343(10), 643–646 (2006)

  2. Diagana, T.: Weighted pseudo-almost periodic solutions to some differential equations. Nonlinear Anal. TMA 68, 2250–2260 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blot, J., Cieutat, P., Ezzinbi, K.: New approach for weighted pseudo almost periodic functions under the light of measure theory, basic results and applications, Applicable Analysis. (2012) (in press)

  4. Blot, J., Cieutat, P., Ezzinbi, K.: Measure theory and pseudo almost automorphic functions: new developments and applications. Nonlinear Anal. TMA 75, 2426–2447 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chang, Y.K., Zhao, Z.H., Nieto, J.J.: Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential equations in Hilbert spaces. Rev. Mat. Complut. 24, 421–438 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhang, R., Chang, Y.K., N’Guérékata, G.M.: New composition theorems of Stepanov-like weighted pseudo almost automorphic functions and applications to nonautonomous evolution equations. Nonlinear Anal. RWA 13, 2866–2879 (2012)

    Article  MATH  Google Scholar 

  7. Ji, D., Zhang, C.: Translation invariance of weighted pseudo almost periodic functions and related problems. J. Math. Anal. Appl. 391, 350–362 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang, L.L., Li, H.X.: Weighted pseudo almost periodic solutions of second order neutral differential equations with piecewiseconstant argument. Nonlinear Anal. TMA 74, 6770–6780 (2011)

    Article  MATH  Google Scholar 

  9. Zhang, L.L., Li, H.X.: Weighted pseudo almost periodic solutions of second-order neutral-delay differential equations with piecewise constant argument. Comput. Math. Appl. 62, 4362–4376 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, X., Hu, X.: Weighted pseudo almost periodic solutions of neutral functional differential equations. Nonlinear Anal. RWA 12, 601–610 (2011)

    Article  MATH  Google Scholar 

  11. Ding, H.S., Liang, J., Xiao, T.J.: Weighted pseudo almost automorphic functions and application to semilinear evolution equations (2011) ( preprint)

  12. Boza, S., Soria, J.: Weighted weak modular and norm inequalities for the Hardy operator in variable \(L^p\) spaces of monotone functions. Rev. Mat. Complut. 25, 459–474 (2012)

    Article  MathSciNet  Google Scholar 

  13. Cruz-Uribe, D., Mamedov, F.I.: On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces. Rev. Mat. Complut. 25, 335–367 (2012)

    Article  MathSciNet  Google Scholar 

  14. Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control system. Science 197, 287–289 (1977)

    Article  Google Scholar 

  15. Alzabut, J.O., Nieto, J.J., Stamov, G.Tr.: Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis. Bound. Value Probl. p. 10 (2009) (Art. ID 127510)

  16. Braverman, E., Saker, S.H.: Permanence, oscillation and attractivity of the discrete hematopoiesis model with variable coefficients. Nonlinear Anal. TMA 67, 2955–2965 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Saker, S.H., Alzabut, J.O.: On the impulsive delay hematopoiesis model with periodic coefficients. Rocky Mountain J. Math. 39, 1657–1688 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Padhi, S., Srivastava, S., Dix, J.G.: Existence of three nonnegative periodic solutions for functional differential equations and applications to hematopoiesis. Panamer. Math. J. 19, 27–36 (2009)

    MathSciNet  MATH  Google Scholar 

  19. Li, Y., Wang, C.: Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales. Adv. Differ. Equ. 2012, 77 (2012)

    Article  Google Scholar 

  20. Long, F.: Positive almost periodic solution for a class of Nicholson’s blowflies model with a linear harvesting term. Nonlinear Anal. RWA 13, 686–693 (2012)

    Article  MATH  Google Scholar 

  21. Blot, J., Pennequin, D.: Existence and structure results on almost periodic solutions of difference equations. J. Differ. Equ. Appl. 7, 383–402 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pennequin, D.: Existence of almost periodic solutions of discrete time equations. Discret. Contin. Dynam. Syst. 7, 51–60 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Araya, D., Castro, R., Lizama, C.: Almost automorphic solutions of difference equations. Adv. Differ. Equ. 2009. p. 15 (2009), (Art. ID 591380)

  24. Cuevas, C., Henríquez, H., Lizama, C.: On the existence of almost automorphic solutions of volterra difference equations. J. Differ. Equ. Appl. 18(11), 1931–1946 (2012)

    Google Scholar 

  25. Nguyen Van Minh, On the asymptotic behavior of volterra difference equations (preprint). http://arxiv.org/abs/1010.5454

  26. Ding, H.S., Fu, J.D., N’Guérékata, G.M.: Positive almost periodic type solutions to a class of nonlinear difference equations. Electron. J. Qual. Theory Differ. Equ. 25, 1–16 (2011)

    MATH  Google Scholar 

  27. Deimling, K.: Nonlinear functionl analysis. Springer, New York (1985)

    Book  Google Scholar 

  28. Li, K., Liang, J., Xiao, T.J.: New existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation. J. Math. Anal. Appl. 328, 753–766 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Corduneanu, C.: Almost periodic functions, 2nd edn. Chelsea, New York (1989)

    MATH  Google Scholar 

  30. Diagana, T.: Pseudo almost periodic functions in Banach spaces. Nova Science Publishers, Inc., New York (2007)

  31. Zhang, C.: Almost periodic type functions and ergodicity. Kluwer Academic Publishers, Dordrecht (2003)

    Book  MATH  Google Scholar 

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Acknowledgments

The authors thank the referees for their valuable comments that helped to improve the text. The work was supported by the NSF of China (11101192), the Key Project of Chinese Ministry of Education (211090), the NSF of Jiangxi Province (20114BAB211002), the Jiangxi Provincial Education Department (GJJ12173), and the Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University.

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Correspondence to Hui-Sheng Ding.

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Ding, HS., N’Guérékata, G.M. & Nieto, J.J. Weighted pseudo almost periodic solutions for a class of discrete hematopoiesis model. Rev Mat Complut 26, 427–443 (2013). https://doi.org/10.1007/s13163-012-0114-y

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  • DOI: https://doi.org/10.1007/s13163-012-0114-y

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