Abstract
In this article we introduce a new definition of impulsive conditions for boundary value problems of first order impulsive integro-differential equations with multi-point boundary conditions. By using the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, we obtain the extremal solutions of the boundary value problem. An example is also discussed to illustrate our results. Mathematics Subject Classification 2010: 34B15; 34B37.
Highlights
Impulsive differential equations describe processes which have a sudden change of their state at certain moments
Impulse effects are important in many real world applications, such as physics, medicine, biology, control theory, population dynamics, etc
Boundary value problems for first order impulsive functional differential equations with lower and upper solutions in reversed order have been widely discussed in recent years
Summary
Impulsive differential equations describe processes which have a sudden change of their state at certain moments. We consider the following boundary value problem for first order impulsive integro-differential equations (BVP): Boundary value problems for first order impulsive functional differential equations with lower and upper solutions in reversed order have been widely discussed in recent years (see [15-20]).
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