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A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments. (English) Zbl 1259.45008
The paper is concerned with a class of boundary value problems for nonlinear mixed impulsive integro-differential equations with deviating arguments. The authors review existing results and current interest in these problems before going on to derive some new theory. The main results of the paper concern the use of the method of upper and lower solutions with a monotone iterative technique. The minimal and maximal solutions are exhibited as the limits of monotone sequences of functions. The paper concludes with an example.
MSC:
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations