On a nonlocal problem for impulsive differential equations with mixed maxima

Abstract

A nonlocal boundary value problem for a first order system of ordinary integro-differential equations with impulsive effects and mixed 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.

Keywords

• impulsive integro-differential equations
• nonlocal boundary condition
• mixed maxima
• successive approximations
• existence and uniqueness of solution
• continuous dependence of solution
• импульсные интегро-дифференциальные уравнения
• нелокальные граничные условия
• смешанные максимумы
• последовательные приближения
• существование и единственность решения
• непрерывная зависимость решения