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Asymptotically Almost Periodic Solutions of Equations with Delays and Nonfixed Times of Pulse Action

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By using the properties of asymptotically almost periodic solutions, we prove the theorems on existence of an asymptotically stable piecewise continuous solution of a system of differential equations with delays and nonfixed times of pulse action.

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References

  1. R. Hakl, M. Pinto, V. Tkachenko, and S. Trofimchuk. “Almost periodic evolution systems with impulse action at state-dependent moments,” J. Math. Anal. Appl., 446, 1030–1045 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  2. H. R. Henriquez, B. De Andrade, and M. Rabelo, “Existence of almost periodic solutions for a class of abstract impulsive differential equations,” ISRN Math. Anal. (2011), Article ID 632687.

  3. M. Pinto and G. Robledo, “Existence and stability of almost periodic solutions in impulsive neural network models,” Appl. Math. Comput., 217, No. 8, 4167–4177 (2010).

    MathSciNet  MATH  Google Scholar 

  4. A. M. Samoilenko and S. I. Trofimchuk, “Almost periodic impulsive systems,” Different. Equat., 29, 684–691 (1993).

    MATH  Google Scholar 

  5. G. T. Stamov, Almost Periodic Solutions of Impulsive Differential Equations, Springer, Berlin (2012).

    Book  MATH  Google Scholar 

  6. V. Tkachenko, “Almost periodic solutions of parabolic-type equations with impulsive action,” Funct. Different. Equat., 21, No. 3–4, 155–169 (2014).

    MathSciNet  MATH  Google Scholar 

  7. V. I. Tkachenko, “Exponential dichotomy and existence of almost periodic solutions of impulsive differential equations,” Nelin. Kolyv., 17, No. 4, 546–557 (2014); English translation : J. Math. Sci., 212, No. 4, 490–502 (2016).

  8. V. Tkachenko, “Almost periodic solutions of evolution differential equations with impulsive action,” in: Mathematical Modeling and Applications in Nonlinear Dynamics, Springer, New York (2016), pp. 161–205.

  9. Q. Wang, H. Zhang, M. Ding, and Z. Wang, “Global attractivity of the almost periodic solution of a delay logistic population model with impulses,” Nonlinear Anal., 73, 3688–3697 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Halanay and D. Wexler, Teoria Calitativǎ a Sistemelor cu Impulsuri, Editura Academiei Republicii Socialiste România, Bucureşti (1968).

    MATH  Google Scholar 

  11. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific Publishing, Singapore (1995).

    Book  MATH  Google Scholar 

  12. T. Yoshizawa, “Asymptotically almost periodic solutions of an almost periodic system,” Funkc. Ekvacioj, 12, 23–40 (1969).

    MathSciNet  MATH  Google Scholar 

  13. Yu. M. Myslo and V. I. Tkachenko, “Global attractivity in almost periodic single species models,” Funct. Different. Equat., 18, No. 3–4, 269–278 (2011).

    MathSciNet  MATH  Google Scholar 

  14. A. M. Samoilenko, N. A. Perestyuk, and S. I. Trofimchuk, “Generalized solutions of impulse systems and the phenomenon of pulsations,” Ukr. Mat. Zh., 43, No. 5, 657–663 (1991); English translation : Ukr. Math. J., 43, No. 5, 610–615 (1991).

  15. X. Liu and G. Ballinger, “Existence and continuability of solutions for differential equations with delays and state-dependent impulses,” Nonlinear Anal.: Theory, Meth. Appl., 51, No. 4, 633–647 (2004).

  16. M. U. Akhmetov and N. A. Perestyuk, “Periodic and almost periodic solutions of strongly nonlinear impulse systems,” J. Appl. Math. Mech., 56, No. 6, 829–837 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  17. A. M. Samoilenko and S. I. Trofimchuk, “Unbounded functions with almost periodic differences,” Ukr. Mat. Zh., 43, No. 10, 1409–1413 (1991); English translation : Ukr. Math. J., 43, No. 10, 1306–1309 (1991).

  18. N. A. Perestyuk and M. U. Akhmetov, “Almost periodic solutions of impulse systems,” Ukr. Mat. Zh., 39, No. 1, 74–80 (1987); English translation : Ukr. Math. J., 39, No. 1, 61–66 (1987).

  19. A. M. Fink, Almost Periodic Differential Equations, Springer, Berlin (1974).

    Book  MATH  Google Scholar 

  20. A. M. Samoilenko and S. I. Trofimchuk, “Spaces of piecewise-continuous almost periodic functions and of almost periodic sets on the line. I,” Ukr. Mat. Zh., 43, No. 12, 1613–1619 (1991; English translation : Ukr. Math. J., 43, No. 12, 1501–1506 (1991).

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Translated from Neliniini Kolyvannya, Vol. 19, No. 4, pp. 533–546, October–December, 2016.

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Myslo, Y.M., Tkachenko, V.I. Asymptotically Almost Periodic Solutions of Equations with Delays and Nonfixed Times of Pulse Action. J Math Sci 228, 290–305 (2018). https://doi.org/10.1007/s10958-017-3621-z

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  • DOI: https://doi.org/10.1007/s10958-017-3621-z

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