Email this article Periodic solutions for an impulsive system of integro-differential equations with maxima
- Authors: Yuldashev T.K.1
-
Affiliations:
- National University of Uzbekistan named after Mirzo Ulugbek
- Issue: Vol 26, No 2 (2022)
- Pages: 368-379
- Section: Short Communications
- URL: https://ogarev-online.ru/1991-8615/article/view/104981
- DOI: https://doi.org/10.14498/vsgtu1917
- ID: 104981
Cite item
Full Text
Abstract
A periodical boundary value problem for a first-order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. The obtained system of nonlinear functional-integral equations and the existence and uniqueness of the solution of the periodic boundary value problem are reduced to the solvability of the system of nonlinear functional-integral equations. The method of successive approximations in combination with the method of compressing mapping is used in the proof of one-valued solvability of nonlinear functional-integral equations. We define the way with the aid of which we could prove the existence of periodic solutions of the given periodical boundary value problem.
Full Text
##article.viewOnOriginalSite##About the authors
Tursun K. Yuldashev
National University of Uzbekistan named after Mirzo Ulugbek
Author for correspondence.
Email: tursun.k.yuldashev@gmail.com
ORCID iD: 0000-0002-9346-5362
SPIN-code: 1629-8554
Scopus Author ID: 24482650300
http://www.mathnet.ru/person27151
Dr. Phys. & Math. Sci., Professor, Uzbek-Israel Joint Faculty
Uzbekistan, 4, Vuzgorodok, Universitetskaya st., Tashkent, 100174References
- Anguraj A., Arjunan M. M. Existence and uniqueness of mild and classical solutions of impulsive evolution equations, Electron. J. Diff. Eqns., 2005, vol. 2005, no. 111, pp. 1–8. https://ejde.math.txstate.edu/Volumes/2005/111/abstr.html.
- Ashyralyev A., Sharifov Ya. A. Existence and uniqueness of solutions for nonlinear impulsive differential equations with two–point and integral boundary conditions, Adv. Diff. Eqns., 2013, vol. 2013, 173. DOI: https://doi.org/10.1186/1687-1847-2013-173.
- Ashyralyev A., Sharifov Ya. A. Optimal control problems for impulsive systems with integral boundary conditions, Electron. J. Diff. Eqns., 2013, vol. 2013, no. 80, pp. 1–11. https://ejde.math.txstate.edu/Volumes/2013/80/abstr.html.
- Liu B., Liu X., Liao X. Robust global exponential stability of uncertain impulsive systems, Acta Math. Sci., 2005, vol. 25, no. 1, pp. 161–169. DOI: https://doi.org/10.1016/S0252-9602(17)30273-4.
- Lakshmikantham V., Bainov D. D., Simeonov P. S. Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics, vol. 6. Singapore, World Scientific, 1989, x+273 pp. DOI: https://doi.org/10.1142/0906.
- Mardanov M. J., Sharifov Ya. A., Habib M. H. Existence and uniqueness of solutions for first-order nonlinear differential equations with two-point and integral boundary conditions, Electron. J. Diff. Eqns., 2014, vol. 2014, no. 259, pp. 1–8. https://ejde.math.txstate.edu/Volumes/2014/259/abstr.html.
- Samoilenko A. M., Perestyk N. A. Impulsive Differential Equations, World Scientific Series on Nonlinear Science Series A, vol. 14. Singapore, World Scientific, 1995, ix+462 pp. DOI: https://doi.org/10.1142/2892.
- Sharifov Ya. A. Optimal control problem for the impulsive differential equations with non-local boundary conditions, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, vol. 4(33), pp. 34–45 (In Russian). EDN: RVARRH. DOI: https://doi.org/10.14498/vsgtu1134.
- Sharifov Ya. A. Optimal control for systems with impulsive actions under nonlocal boundary conditions, Russian Math. (Iz. VUZ), 2013, vol. 57, no. 2, pp. 65–72. EDN: XKVHUX. DOI: https://doi.org/10.3103/S1066369X13020084.
- Sharifov Ya. A., Mammadova N. B. Optimal control problem described by impulsive differential equations with nonlocal boundary conditions, Diff. Equ., 2014, vol. 50, no. 3, pp. 401–409. EDN: XLBLAD. DOI: https://doi.org/10.1134/S0012266114030148.
- Sharifov Ya. A. Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions, Ukr. Math. J., 2012, vol. 64, no. 6, pp. 958–970. EDN: XNBIVX DOI: https://doi.org/10.1007/s11253-012-0691-4.
- Yuldashev T. K., Fayziev A. K. On a nonlinear impulsive differential equations with maxima, Bull. Inst. Math., 2021, vol. 4, no. 6, pp. 42–49.
- Yuldashev T. K., Fayziev A. K. On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima, Nanosyst., Phys. Chem. Math., 2022, vol. 13, no. 1, pp. 36–44. EDN: SHAUGO DOI: https://doi.org/10.17586/2220-8054-2022-13-1-36-44.
- Bai Ch., Yang D. Existence of solutions for second-order nonlinear impulsive differential equations with periodic boundary value conditions, Bound. Value Probl., 2007, vol. 2007, 41589. DOI: https://doi.org/10.1155/2007/41589.
- Chen J., Tisdell C. C., Yuan R. On the solvability of periodic boundary value problems with impulse, J. Math. Anal. Appl., 2007, vol. 331, no. 2, pp. 902–912. DOI: https://doi.org/10.1016/j.jmaa.2006.09.021.
- Li X., Bohner M., Wang Ch.-K. Impulsive differential equations: Periodic solutions and applications, Automatica, 2015, vol. 52, pp. 173–178. DOI: https://doi.org/10.1016/j.automatica.2014.11.009.
- Hu Z., Han M. Periodic solutions and bifurcations of first order periodic impulsive differential equations, Int. J. Bifurcation Chaos Appl. Sci. Eng., 2009, vol. 19, no. 8, pp. 2515–2530. DOI: https://doi.org/10.1142/S0218127409024281.
- Yuldashev T. K. Limit value problem for a system of integro-differential equations with two point mixed maximums, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2008, no. 1(16), pp. 15–22 (In Russian). EDN: JTBCJT. DOI: https://doi.org/10.14498/vsgtu567.
Supplementary files
