Integral Condition with Nonlinear Kernel for an Impulsive System of Differential Equations with Maxima and Redefinition Vector

• Published in: Lobachevskii journal of mathematics Vol. 43; no. 8; pp. 2332 - 2340
• Main Authors: Yuldashev, T. K., Fayziyev, A. K.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.08.2022; Springer Nature B.V
• Subjects: Algebra; Analysis; Boundary value problems; Differential equations; Geometry; Integral equations; Kernels; Mathematical analysis; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Probability Theory and Stochastic Processes; existence and uniqueness of solution; impulsive differential equations; nonlinear kernel; nonlinear maxima; nonlocal integral condition
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080222110312

A nonlocal integral problem for a system of ordinary differential equations with impulsive effects, nonlinear maxima and redefinition vector is investigated. The nonlocal inverse boundary value problem is given by the integral condition with nonlinear kernel. This problem is reduced to investigate of solvability of nonlinear functional-integral equations with nonlinear maxima. In proofing of the theorem on one valued solvability is used the method of successive approximations in combination it with the method of compressing mapping. The existence and uniqueness of the solution of the inverse boundary value problem are proved.