NONLOCAL BOUNDARY VALUE PROBLEM FOR A NONLINEAR IMPULSIVE INTEGRO-DIFFERENTIAL SYSTEM WITH MAXIMA
DOI:
https://doi.org/10.55439/yutsftim/583Kalit so‘zlar:
impulsive integro-differential equations, nonlocal boundary condition, successive approximations, existence and uniqueness of solution, continuous dependence of solutionAbstrak
A nonlocal boundary value problem for a first order system of ordinary
integro-differential equations with impulsive effects and maxima is investigated. The
boundary value problem is given by the integral condition. The method of successive
approximations in combination it with the method of compressing mapping is used.
The existence and uniqueness of the solution of the boundary value problem are
proved. The continuous dependence of the solutions on the right-hand side of the
boundary condition is showed.
References
Benchohra M., Henderson J., Ntouyas S.K. Impulsive differential equations and inclusions. Contemporary mathematics and its application. New York: Hindawi Publishing Corporation, 2006.
Boichuk A.A., Samoilenko A.M. Generalized inverse operators and fredholm boundary-value problems. Utrecht; Brill, 2004.
Boichuk A.A., Samoilenko A.M. Generalized inverse operators and Fredholm boundary-value problems (2nd ed.). Berlin - Boston: Walter de Gruyter GmbH, 2016. 314p.
Assanova A. An integral-boundary value problem for a partial differential equation of second order. Turkish Journal of Mathematics, 2019, vol. 43, No 4, P. 1967-1978
Yuldashev T.K. Nonlocal boundary value problem for a nonlinear Fredholm integro-differential equation with degenerate kernel. Differential equations, 2018, vol. 54, No 12, P. 1646-1653
Ashyralyev A., Sharifov Y.A. Optimal control problems for impulsive systems with integral boundary conditions. Elect. J. of Differential Equations, 2013, No. 80, P. 1-11
Bin L., Xinzhi L., Xiaoxin L. Robust global exponential stability of uncertain impulsive systems. Acta Mathematika Scientia, 2005, vol. 25, No 1, P. 161-169.
Yuldashev T.K., Fayziyev A.K. Inverse problem for a second order impulsive system of integro-differential equations with two redefinition vectors and mixed maxima. Nanosystems: Physics, Chemistry, Mathematics. 2023, Volume 14, Issue 1, P.
–21. https://doi.org/10.17586/2220-8054-2023-14-1-13-21 Fayziyev A.K., Abdullozhonova, A. N., Yuldashev T.K. Inverse Problem for Whitham Type Multi-Dimensional Differential Equation with Impulse Effects. Lobachevskii Journal of Mathematics, 2023, Volume 44, Issue 2, P. 570–579. https://doi.org/10.1134/S1995080223020154
