Abstract
In this paper, we investigate a class of first order impulsive integro‐differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.
Highlights
It is well known that the theory of impulsive differential equations is richer than the corresponding theory of differential equations and represent a more natural framework for mathematical modelling of real world phenomena
Many of its branches are still in an initial stage of their development. This is due, to a large extent, to the difficulties created by the special features possessed by impulsive differential equations such as pulse phenomena, confluence and the loss of autonomy
The second order boundary value problems for differential equations, which has been an object of extensive investigation [5 7], can be reduced to first order boundary value problems for integro-differentiM equations
Summary
It is well known that the theory of impulsive differential equations is richer than the corresponding theory of differential equations and represent a more natural framework for mathematical modelling of real world phenomena. We develop monotone iterative technique and show the existence of extremal solutions of a class of periodic boundary value problems for impulsive integro-differential equations. We shall assume that T is continuous and monotone nondecreasing and for any bounded set A C
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