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Affine-Periodic Solutions for Impulsive Differential Systems

  • Wang Chuanbiao [3] ; Yang, Xue [1] ; Chen, Xusheng [2]
    1. [1] Northeast Normal University

      Northeast Normal University

      China

    2. [2] Jilin University

      Jilin University

      China

    3. [3] Communication Unversity of China
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
  • Idioma: inglés
  • DOI: 10.1007/s12346-019-00337-5
  • Enlaces
  • Resumen
    • The affine-periodicity is a new periodic concept which has been founded in recent years. In this paper, we will discuss the existence of affine-periodic solutions for impulsive differential systems. Several existence theorems are proved for dissipative impulsive (functional) differential systems. Some applications are also given by combining Lyapunov’s methods.

  • Referencias bibliográficas
    • 1. Burton, T.A., Zhang, S.: Unified boundedness, periodicity, and stability in ordinary and functional differential equations. Annali di Matematica...
    • 2. Horn, W.A.: Some fixed point theorems for compact maps and flows in banach spaces. Trans. Am. Math. Soc. 149(2), 391–404 (1970). https://doi.org/10.2307/1995402
    • 3. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations, vol. 6. World Scientific, Singapore (1989)
    • 4. Levinson, N.: Transformation theory of non-linear differential equations of the second order. Ann. Math. 45(4), 723–737 (1944). https://doi.org/10.2307/1969299
    • 5. Li, X., Bohner, M., Wang, C.: Impulsive differential equations: periodic solutions and applications. Automatica 52, 173–178 (2015). https://doi.org/10.1016/j.automatica.2014.11.009
    • 6. Li, Y., Huang, F.: Levinsons problem on affine-periodic solutions. Adv. Nonlinear Stud. 15(1), 241–252 (2015). https://doi.org/10.1515/ans-2015-0113
    • 7. Li, Y., Zhou, Q.: Periodic solutions to ordinary differential equations with impulses. Sci. China Ser. A 36(7), 778–790 (1993)
    • 8. Liu, G., Yang, X., Li, Y.: Existence and multiplicity of rotating periodic solutions for resonant hamiltonian systems. J. Differ. Equ....
    • 9. Liu, G., Yang, X., Li, Y.: Rotating periodic solutions for super-linear second order hamiltonian systems. Appl. Math. Lett. (2018). https://doi.org/10.1016/j.aml.2017.11.024
    • 10. Milman, V.D., Myshkis, A.D.: On the stability of motion in the presence of impulses. Sib. Math. J. 1(2), 233–237 (1960)
    • 11. Qian, D., Chen, L., Sun, X.: Periodic solutions of superlinear impulsive differential equations: a geometric approach. J. Differ. Equ....
    • 12. Shen, J., Li, J., Wang, Q.: Boundedness and periodicity in impulsive ordinary and functional differential equations. Nonlinear Anal. TMA...
    • 13. Shen, T., Liu, W.: Infinitely many rotating periodic solutions for suplinear second-order impulsive Hamiltonian systems. Appl. Math. Lett....
    • 14. Wang, C., Li, Y.: Affine-periodic solutions for nonlinear dynamic equations on time scales. Adv. Differ. Equ. 2015(1), 286 (2015). https://doi.org/10.1186/s13662-015-0634-0
    • 15. Wang, C., Yang, X., Li, Y.: Affine-periodic solutions for nonlinear differential equations. Rocky Mt. J. Math. 46(5), 1717–1737 (2016)....
    • 16. Wang, H., Yang, X., Li, Y.: Rotating-symmetric solutions for nonlinear systems with symmetry. Acta Math. Appl. Sin. Engl. Ser. 31(2),...
    • 17. Xing, J., Yang, X., Li, Y.: Rotating periodic solutions for convex hamiltonian systems. Appl. Math. Lett. (2019). https://doi.org/10.1016/j.aml.2018.10.002
    • 18. Yoshizawa, T.: Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, vol. 14. Springer, New York (1975)
    • 19. Zhang, X., Yan, J., Zhan, A.: Existence of positive periodic solutions for an impulsive differential equation. Nonlinear Anal. TMA 68(10),...
    • 20. Zhang, Y., Yang, X., Li, Y.: Affine-periodic solutions for dissipative systems. Abstr. Appl. Anal. (2013). https://doi.org/10.1155/2013/157140

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