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Composition Theorems of Stepanov \(\mu \)-Pseudo Almost Automorphic Functions and Applications to Nonautonomous Neutral Evolution Equations

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Abstract

In this work, we present a new composition theorem of \(\mu \)-pseudo almost automorphic functions in the sense of Stepanov satisfying some local Lipschitz conditions. Using this results, we establish an existence result of \(\mu \)-pseudo almost automorphic solutions for some nonautonomous neutral partial evolution equation with Stepanov \(\mu \)-pseudo almost automorphic nonlinearity. An example is shown to illustrate our results.

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References

  1. Acquistapace, P., Terreni, B.: A unified approach to abstract linear nonautonomous parabolic equations. Rendiconti del Seminario Matematico della Università di Padova 78, 47–107 (1987)

    MathSciNet  MATH  Google Scholar 

  2. Baroun, M., Boulite, S., N’Guérékata, G.M., Maniar, L.: Almost automorphy of semilinear parabolic evolution equations. Electron. J. Differ. Equ. 2008(60), 1–9 (2008)

    MathSciNet  MATH  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  MATH  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. Applicable Anal. 2011, 1–34 (2011)

  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  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Diagana, T.: Weighted pseudo almost periodic functions and applications. Comptes Rendus de l’Académie des Sciences 343(10), 643–646 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Diagana, T.: Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations. Nonlinear Anal. 69, 4277–4285 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ding, H.S., Liang, J., N’Guerekata, G.M., Xiao, T.J.: Pseudo almost periodicity of some nonautonomous evolution equations with delay. Nonlinear Anal. 67, 1412–1418 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ding, H.S., Long, W., N’guérékata, G.M.: A composition theorem for weighted pseudo-almost automorphic functions and applications. Nonlinear Anal. 73, 2644–2650 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Engel, K.J., Nagel, R.: One Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics. Springer, Berlin (2000)

    MATH  Google Scholar 

  13. Fan, Z., Liang, J., Xiao, T.J.: Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations. Nonlinear Anal. 13, 131–140 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hu, Z.R., Jin, Z.: Stepanov-like pseudo almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay. Nonlinear Anal. 71, 5381–5391 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hu, Z., Jin, Z.: Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations. Nonlinear Anal. 71, 2349–2360 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hu, Z., Jin, Z.: Stepanov-like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations. Nonlinear Anal. 75, 244–252 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lee, H., Alkahby, H.: Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay. Nonlinear Anal. 69, 2158–2166 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, H.X., Li, L.L.: Stepanov-like pseudo almost periodicity and semilinear differential equations with uniform continuity. Results Math. 59, 43–61 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  20. N’Guerekata, G.M., Pankov, A.: Stepanov-like almost automorphic functions and monotone evolution equations. Nonlinear Anal. 68, 2658–2667 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Xiao, T.J., Zhu, X.X., Liang, J.: Pseudo almost automorphic mild solutions to nonautonomous differential equations and applications. Nonlinear Anal. 70, 4079–4085 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakesh, Morocco

    Abdelkarim-Nidal Akdad, Brahim Essebbar & Khalil Ezzinbi

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  1. Abdelkarim-Nidal Akdad
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  2. Brahim Essebbar
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  3. Khalil Ezzinbi
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Correspondence to Khalil Ezzinbi.

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Akdad, AN., Essebbar, B. & Ezzinbi, K. Composition Theorems of Stepanov \(\mu \)-Pseudo Almost Automorphic Functions and Applications to Nonautonomous Neutral Evolution Equations. Differ Equ Dyn Syst 25, 397–416 (2017). https://doi.org/10.1007/s12591-015-0246-x

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