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Pseudo Almost Periodic Solutions to a Class of Semilinear Differential Equations

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An Erratum to this article was published on 25 January 2007

Abstract

This paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to a class of semilinear differential equations involving the algebraic sum of two (possibly noncommuting) densely defined closed linear operators acting on a Hilbert space. Sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those semilinear equations are obtained.

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References

  1. Diagana, T., ‘Pseudo almost periodic solutions to some differential equations’, Nonlinear Analysis 60(7), 2005, 1277–1286.

    Article  MathSciNet  MATH  Google Scholar 

  2. Diagana, T., ‘Some remarks on some second-order hyperbolic differential equations’, Semigroup Forum 68(3), 2004, 357–364.

    Article  MathSciNet  MATH  Google Scholar 

  3. Diagana, T. and N'Guérékata, G. M., ‘Some extension of the Bohr-Neugebauer-N'Guerekata Theorem’, Journal of Analysis and Applications 2(1), 2004, 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  4. N'Guérékata, G. M., Topics in Almost Automorphy, Springer, New York, 2005.

    Google Scholar 

  5. Zhang, C. Y., ‘Pseudo almost periodic solutions of some differential equations’, Journal of Mathematical Analysis and Application 151, 1994, 62–76.

    Article  Google Scholar 

  6. Zhang, C. Y., ‘Pseudo almost periodic solutions of some differential equations II’, Journal of Mathematical Analysis and Application 192, 1995, 543–561.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang, C. Y., ‘Integration of vector-valued pseudo almost periodic functions’, Proceedings of the American Mathematical Society 121, 1994, 167–174.

  8. Corduneanu, C., Almost Periodic Functions, 2nd edn., Chelsea, New York, 1989.

  9. Fink, A. M., Almost Periodic Differential Equations, Lecture Notes in Mathematics 377, Springer-Verlag, New York-Berlin, 1974.

  10. N'Guérékata, G. M., Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces, Kluwer Academic/Plenum Publishers, New York, 2001.

    Google Scholar 

  11. Ait Dads, E., Ezzinbi, K., and Arino, O., ‘Pseudo almost periodic solutions for some differential equations in a banach space’, Nonlinear Analysis 28(7), 1997, 1141–1155.

    Article  MathSciNet  Google Scholar 

  12. Ait Dads, E. and Arino, O., ‘Exponential dichotomy and existence of pseudo almost periodic solutions of some differential equations’, Nonlinear Analysis 27(4), 1996, 369–386.

    Article  MathSciNet  MATH  Google Scholar 

  13. Amir, B. and Maniar, L., ‘Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain’, Annales Mathematiques Blaise Pascal 6(1), 1999, 1–11.

    MathSciNet  MATH  Google Scholar 

  14. Cuevas, C. and Pinto, M., ‘Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non-dense domain’, Nonlinear Analysis 45, 2001, 73–83.

    Article  MathSciNet  MATH  Google Scholar 

  15. Hino, Y., Naito, T., Minh, N. V., and Shin, J. S., Almost Periodic Solutions of Differential Equations in Banach Spaces, Stability and Control: Theory, Methods and Applications, vol. {15}, Taylor and Francis, London, 2002.

    Google Scholar 

  16. Huang, F. L., Li, H. X., and Li, J. Y., ‘Composition of pseudo almost-periodic functions and semilinear differential equations’, Journal of Mathematical Analysis and Application 255(2), 2001, 436–446.

    Article  MathSciNet  MATH  Google Scholar 

  17. Zaidman, S., Topics in Abstract Differential Equations, Pitman Research Notes in Mathematics Ser. II, John Wiley and Sons, New York, 1994–1995.

    Google Scholar 

  18. Locker, J., Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators, AMS Mathematical Surveys and Monographs, vol. 73, 2000.

  19. Diagana, T., N'Guérékata, G. M., and Minh, N. V., ‘Almost Automorphic Solutions of Evolution Equations’, Proceedings of the American Mathematical Society 134(11), 2004, 3289–3298.

  20. Diagana, T. and N'Guérékata, G. M., ‘On some perturbations of some abstract differential equations’, Comment. Math. Prace Mat. XLIII(2), 2003, 201–206.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Howard University, 2441, 6th Street N.W., Washington, D.C., 20059, USA

    Toka Diagana

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  1. Toka Diagana
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Correspondence to Toka Diagana.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s11071-006-9159-0.

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Diagana, T. Pseudo Almost Periodic Solutions to a Class of Semilinear Differential Equations. Nonlinear Dyn 45, 45–53 (2006). https://doi.org/10.1007/s11071-005-1890-4

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  • DOI: https://doi.org/10.1007/s11071-005-1890-4

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