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New Results for Some Neutral Partial Functional Differential Equations

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Abstract

In this research work, we study some new results for the existence and uniqueness of doubly measures pseudo almost automorphic and pseudo almost periodic solutions for some neutral partial functional differential equations in Hilbert spaces. The main results of this paper are based on the compositional theorem and the Banach fixed point theorem. Some examples are given to illustrate the theory.

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References

  1. Ait Dads, E., Ezzinbi, K., Miraoui, M.: \((\mu,\nu )-\)Pseudo almost automorphic solutions for some nonautonomous differential equations. Int. J. Math. 26, 1–21 (2015)

    Article  Google Scholar 

  2. Ben-Salah, M., Ezzinbi, K., Rebey, A.: Pseudo almost periodic and pseudo almost automorphic solutions to evolution equations in Hilbert spaces. Mediterr. J. Math. 13(2), 703–717 (2016)

    Article  MathSciNet  Google Scholar 

  3. Blot, J., Mophou, G.M., N’Guérékata, G.M., Pennequin, D.: Weighted pseudo almost automorphic functions and applications to abstract differential equations. Nonlinear Anal. 71, 903–909 (2009)

    Article  MathSciNet  Google Scholar 

  4. Blot, J., Cieutat, P., Ezzinbi, K.: New approach for weighted pseudo almost periodic functions under the light of measure theory, basic results and applications. Appl. Anal. 92(3), 493–526 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Bochner, S.: Continuous mappings of almost automorphic and almost periodic functions. Proc. Natl. Acad. Sci. USA 52, 907–910 (1964)

    Article  MathSciNet  Google Scholar 

  7. 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(2), 421–438 (2011)

    Article  MathSciNet  Google Scholar 

  8. Chang, Y.K., Zhao, Z.H., Nieto, J.J., Liu, Z.W.: Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a partial functional differential equation in Banach spaces. J. Nonlinear Sci. Appl. 5, 14–26 (2012)

    Article  MathSciNet  Google Scholar 

  9. Chérif, F., Miraoui, M.: New results for a Lasota–Wazewska model. Int. J. Biomath. 12(2), 1950019 (2019)

    Article  MathSciNet  Google Scholar 

  10. Corduneanu, C.: Almost Periodic Functions. Wiley, New York (1968). (Reprinted, Chelsea, New York 1989)

    MATH  Google Scholar 

  11. Diagana, T.: Pseudo almost periodic solutions to some differential equations. Nonlinear Anal. Theory Methods Appl. 60(7), 1277–1286 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Diagana, T., Ezzinbi, K., Miraoui, M.: Pseudo-almost periodic and pseudo-almost automorphic solutions to some evolution equations involving theoretical measure theory. Cubo 16(2), 1–31 (2014)

    Article  MathSciNet  Google Scholar 

  14. Ding, H.S., Liu, Q.L., Nieto, J.J.: Existence of positive almost periodic solutions to a class of hematopoiesis model. Appl. Math. Model. 40(4), 3289–3297 (2016)

    Article  MathSciNet  Google Scholar 

  15. Ezzinbi, K., Toure, H., Zabsonre, I.: Weighted pseudo almost periodic and pseudo almost automorphic solutions of class r for some partial differential equations. Differ. Equ. Dyn. Syst. (2018). https://doi.org/10.1007/s12591-018-00447-7

    Article  MATH  Google Scholar 

  16. Kostić, M.: Generalized almost automorphic and generalized asymptotically almost automorphic solutions of abstract volterra integro-differential. Fract. Differ. Calc. (2018). https://doi.org/10.7153/fdc-2018-08-16

    Article  MathSciNet  MATH  Google Scholar 

  17. Miraoui, M.: Existence of \(\mu -\)pseudo almost periodic solutions to some evolution equations. Math. Methods Appl. Sci. 40(13), 4716–4726 (2017)

    MathSciNet  MATH  Google Scholar 

  18. Miraoui, M.: Pseudo almost automorphic solutions for some differential equations with reflection of the argument. Numer. Funct. Anal. Optim. 38(3), 376–394 (2017)

    Article  MathSciNet  Google Scholar 

  19. Miraoui, M., Ezzinbi, K., Rebey, A.: \(\mu -\)Pseudo almost periodic solutions in \(\alpha -\)norm to some neutral partial differential equations with finite delay. Dynamics of continuous discrete and impulsive systems. Canada 24, 83–96 (2017)

    MATH  Google Scholar 

  20. Miraoui, M., Yaakobi, N.: Measure pseudo almost periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Numer. Funct. Anal. Optim. 40(5), 571–585 (2019)

    Article  MathSciNet  Google Scholar 

  21. N’Guérékata, G.M.: Almost Automorphic and Almost Periodic Functions in Abstract Spaces. Kluwer Academic Publishers, New-York (2001)

    Book  Google Scholar 

  22. N’Guérékata, G.M.: Topics in Almost Automorphy. Springer, New York (2005)

    MATH  Google Scholar 

  23. Zhang, C.Y.: Pseudo almost periodic solutions of some differential equations. J. Math. Anal. Appl. 151, 62–76 (1994)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. UR Analysis and Control of PDEs, UR13ES64, FSM, University of Monastir, Monastir, Tunisia

    Mounir Ben-Salah

  2. IPEIK, University of Kairouan, Kairouan, Tunisia

    Mounir Ben-Salah & Mohsen Miraoui

  3. LR11ES53, University of Sfax, Sfax, Tunisia

    Mohsen Miraoui

  4. ISMAIK, University of Kairouan, Kairouan, Tunisia

    Amor Rebey

  5. Majmaah University, Al Majmaah, Saudi Arabia

    Amor Rebey

Authors
  1. Mounir Ben-Salah
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  2. Mohsen Miraoui
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  3. Amor Rebey
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Correspondence to Mohsen Miraoui.

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Ben-Salah, M., Miraoui, M. & Rebey, A. New Results for Some Neutral Partial Functional Differential Equations. Results Math 74, 181 (2019). https://doi.org/10.1007/s00025-019-1106-8

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