Advanced Search
Article Contents
Article Contents

$ (\omega,\mathbb{T}) $-periodic solutions of impulsive evolution equations

  • * Corresponding author: JinRong Wang

    * Corresponding author: JinRong Wang
Abstract Full Text(HTML) Related Papers Cited by
  • In this paper, we study $ (\omega,\mathbb{T}) $-periodic impulsive evolution equations via the operator semigroups theory in Banach spaces $ X $, where $ \mathbb{T}: X\rightarrow X $ is a linear isomorphism. Existence and uniqueness of $ (\omega,\mathbb{T}) $-periodic solutions results for linear and semilinear problems are obtained by Fredholm alternative theorem and fixed point theorems, which extend the related results for periodic impulsive differential equations.

    Mathematics Subject Classification: 34A37, 93B05, 93C25.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] N. U. AhmedK. L. Teo and S. H. Hou, Nonlinear impulsive systems on infinite dimensional spaces, Nonlinear Analysis: TMA, 54 (2003), 907-925.  doi: 10.1016/S0362-546X(03)00117-2.
    [2] E. Alvarez, A. Gómez and M. Pinto, $(\omega, c)$-periodic functions and mild solutions to abstract fractional integro-differential equations, Electron. J. Qual. Theory Differ. Equ., (2018), 16–24. doi: 10.14232/ejqtde.2018.1.16.
    [3] M. AgaoglouM. Fečkan and A. Panagiotidou, Existence and uniqueness of $(\omega, c)$-periodic solutions of semilinear evolution equations, Int. J. Dynamical Systems and Differential Equations, 10 (2020), 149-166.  doi: 10.1504/IJDSDE.2020.106027.
    [4] E. Alvarez, S. Castillo and M. Pinto, $(\omega, c)-$Pseudo periodic functions, first order Cauchy problem and Lasota-Wazewska model with ergodic and unbounded oscillating production of red cells, Bound. Value Prob., (2019), 106–126. doi: 10.1186/s13661-019-1217-x.
    [5] E. AlvarezS. Castillo and M. Pinto, $(\omega, c)-$asymptotically periodic functions, first-order Cauchy problem, and Lasota-Wazewska model with unbounded oscillating production of red cells, Math. Meth. Appl. Sci., 43 (2020), 305-319.  doi: 10.1002/mma.5880.
    [6] D. Bainov and P. Simeonov, Theory of Impulsive Differential Equations, Series on Advances in Mathematics for Applied Sciences, vol. 28. Singapore, World Scientifc, 1995. doi: 10.1142/9789812831804.
    [7] D. Bainov and P. Simeonov, Oscillation Theory of Impulsive Differential Equations, Interna-tional Publications, 1998.
    [8] C. Cooke and J. Kroll, The existence of periodic solutions to certain impulsive differential equations, Comput. Math. Appl., 44 (2002), 667-676.  doi: 10.1016/S0898-1221(02)00181-5.
    [9] X. Chang and Y. Li, Rotating periodic solutions of second order dissipative dynamical systems, Discret. Contin. Dyn. Syst., 36 (2016), 633-652. 
    [10] M. FečkanJ. Wang and Y. Zhou, Existence of periodic solutions for nonlinear evolution equations with non- instantaneous impulses, Nonauton. Dyn. Syst., 1 (2014), 93-101. 
    [11] M. FečkanR. Ma and B. Thompson, Forced symmetric oscillations, Bull. Belg. Math. Soc., 14 (2007), 73-85.  doi: 10.36045/bbms/1172852245.
    [12] Y. LiF. CongZ. Lin and W. liu, Periodic solutions for evolution equations, Nonlinear Analysis: Theory, Methods and Applications, 36 (1999), 275-293.  doi: 10.1016/S0362-546X(97)00626-3.
    [13] X. LiB. Martin and C. Wang, Impulsive differential equations: Periodic solutions and applications, Automatica, 52 (2015), 173-178.  doi: 10.1016/j.automatica.2014.11.009.
    [14] M. LiJ. Wang and M. Fečkan, $(\omega, c)$-periodic solutions for impulsive differential systems, Communications Mathematical Analysis, 21 (2018), 35-46. 
    [15] K. LiuJ. WangD. O'Regan and M. Fečkan, A new class of $(\omega, c)$-periodic non-instantaneous impulsive differential equations, Mediterr. J. Math., 17 (2020), 155-177.  doi: 10.1007/s00009-020-01574-8.
    [16] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4612-5561-1.
    [17] A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. doi: 10.1142/9789812798664.
    [18] C. Wang, Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 2828-2842.  doi: 10.1016/j.cnsns.2013.12.038.
    [19] J. Wang and M. Fečkan, A general class of impulsive evolution equations, Topol. Meth. Nonlinear Anal., 46 (2015), 915-934. 
    [20] J. Wang, X. Xiang and W. Wei, Linear impulsive periodic system with time-varying generating operators on Banach space, Adv. Differ. Equ., (2007), 26196, 16 pp. doi: 10.1155/2007/26196.
  • 加载中

Article Metrics

HTML views(888) PDF downloads(433) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint