Geodesic
Periodic solutions for an impulsive system of~integro-differential equations with maxima
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 368-379.

Voir la notice de l'article provenant de la source Math-Net.Ru

A periodical boundary value problem for a first-order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. A system of nonlinear functional-integral equations is obtained 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.
Keywords: impulsive integro-differential equations, periodical boundary value condition, nonlinear kernel, compressing mapping, existence and uniqueness of periodic solution. 
@article{VSGTU_2022_26_2_a9,
     author = {T. K. Yuldashev},
     title = {Periodic solutions for an impulsive system of~integro-differential equations with maxima},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {368--379},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a9/}
}
TY  - JOUR
AU  - T. K. Yuldashev
TI  - Periodic solutions for an impulsive system of~integro-differential equations with maxima
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2022
SP  - 368
EP  - 379
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a9/
LA  - en
ID  - VSGTU_2022_26_2_a9
ER  - 
%0 Journal Article
%A T. K. Yuldashev
%T Periodic solutions for an impulsive system of~integro-differential equations with maxima
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2022
%P 368-379
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a9/
%G en
%F VSGTU_2022_26_2_a9
T. K. Yuldashev. Periodic solutions for an impulsive system of~integro-differential equations with maxima. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 368-379. http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a9/

[1] Anguraj A., Arjunan M. M., “Existence and uniqueness of mild and classical solutions of impulsive evolution equations”, Electron. J. Diff. Eqns., 2005:111 (2005), 1–8 https://ejde.math.txstate.edu/Volumes/2005/111/abstr.html

[2] 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 (2013), 173 | DOI

[3] Ashyralyev A., Sharifov Ya. A., “Optimal control problems for impulsive systems with integral boundary conditions”, Electron. J. Diff. Eqns., 2013:80 (2013), 1–11 https://ejde.math.txstate.edu/Volumes/2013/80/abstr.html

[4] Liu B., Liu X., Liao X., “Robust global exponential stability of uncertain impulsive systems”, Acta Math. Sci., 25:1 (2005), 161–169 | DOI

[5] Lakshmikantham V., Bainov D. D., Simeonov P. S., Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics, 6, World Scientific, Singapore, 1989, x+273 pp | DOI | Zbl

[6] 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., 2014:259 (2014), 1–8 https://ejde.math.txstate.edu/Volumes/2014/259/abstr.html

[7] Samoilenko A. M., Perestyk N. A., Impulsive Differential Equations, World Scientific Series on Nonlinear Science Series A, 14, World Scientific, Singapore, 1995, ix+462 pp | DOI

[8] 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.], 4(33) (2013), 34–45 (In Russian) | DOI | Zbl

[9] Sharifov Ya. A., “Optimal control for systems with impulsive actions under nonlocal boundary conditions”, Russian Math. (Iz. VUZ), 57:2 (2013), 65–72 | DOI

[10] Sharifov Ya. A., Mammadova N. B., “Optimal control problem described by impulsive differential equations with nonlocal boundary conditions”, Diff. Equ., 50:3 (2014), 401–409 | DOI

[11] Sharifov Ya. A., “Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions”, Ukr. Math. J., 64:6 (2012), 958–970 | DOI

[12] Yuldashev T. K., Fayziev A. K., “On a nonlinear impulsive differential equations with maxima”, Bull. Inst. Math., 4:6 (2021), 42–49

[13] Yuldashev T. K., Fayziev A. K., “On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima”, Nanosyst., Phys. Chem. Math., 13:1 (2022), 36–44 | DOI

[14] Bai Ch., Yang D., “Existence of solutions for second-order nonlinear impulsive differential equations with periodic boundary value conditions”, Bound. Value Probl., 2007 (2007), 41589 | DOI | Zbl

[15] Chen J., Tisdell C. C., Yuan R., “On the solvability of periodic boundary value problems with impulse”, J. Math. Anal. Appl., 331:2 (2007), 902–912 | DOI | Zbl

[16] Li X., Bohner M., Wang Ch.-K., “Impulsive differential equations: Periodic solutions and applications”, Automatica, 52 (2015), 173–178 | DOI | Zbl

[17] Hu Z., Han M., “Periodic solutions and bifurcations of first order periodic impulsive differential equations”, Int. J. Bifurcation Chaos Appl. Sci. Eng., 19:8 (2009), 2515–2530 | DOI | Zbl

[18] 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), 15–22 (In Russian) | DOI