Abstract
This paper is concerned with the existence of extremal solutions of periodic boundary value problems for second-order impulsive integro-differential equations with integral jump conditions. We introduce a new definition of lower and upper solutions with integral jump conditions and prove some new maximum principles. The method of lower and upper solutions and the monotone iterative technique are used. MSC: 34B37; 34K10; 34K45
Highlights
1 Introduction Differential equations which have impulse effects describe many evolution processes that abruptly change their state at a certain moment
Impulsive differential equations have become more important tools in some mathematical models of real processes and phenomena studied in physics, biotechnology, chemical technology, population dynamics and economics; see [ – ]
Many papers have been published about existence analysis of periodic boundary value problems of first and second order for impulsive ordinary or functional or integro-differential equations
Summary
Differential equations which have impulse effects describe many evolution processes that abruptly change their state at a certain moment. The monotone iterative technique coupled with the method of upper and lower solutions has been used to study the existence of extremal solutions of periodic boundary value problems for second-order impulsive equations; see, for example, [ – ]. This method has been used to study abstract nonlinear problems; see [ ]. We consider the periodic boundary value problem for second-order impulsive integro-differential equation (PBVP) with integral jump conditions:. We establish some new comparison principles and discuss the existence and uniqueness of the solutions for second-order impulsive integro-differential equations with integral jump conditions. We give an example to illustrate the obtained results
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