Abstract
In the present paper, a system of nonlinear impulsive differential equations with two-point and integral boundary conditions is investigated. Theorems on the existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.
Highlights
The theory of impulsive differential equations is an important branch of differential equations which has an extensive physical background
Impulsive differential equations arise frequently in the modeling of many physical systems whose states are subject to sudden change at certain moments
We study the existence and uniqueness of the system of nonlinear impulsive differential equations of the type x(t) = f t, x(t) for t = ti, i =, . . . , p, t ∈ [, T], ( )
Summary
The theory of impulsive differential equations is an important branch of differential equations which has an extensive physical background. Impulsive differential equations arise frequently in the modeling of many physical systems whose states are subject to sudden change at certain moments. Boundary value problems with integral conditions constitute a very interesting and important class of problems. They include two-point, three-point, multipoint and nonlocal boundary value problems as special cases. We study the existence and uniqueness of the system of nonlinear impulsive differential equations of the type x(t) = f t, x(t) for t = ti, i = , , . A simple example of application of the main result of this paper is presented
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