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A initial value problems for first-order impulsive differential equations in Banach spaces. (English) Zbl 0985.34049

The authors consider the initial value problem for a first-order integro-ordinary differential equation with impulses at a finite number of prescribed points in a Banach space. They give some preliminary comparison results and then show the existence of minimax quasi-solutions between a pair of quasi-lower and upper solutions to the problem.

MSC:

34G20 Nonlinear differential equations in abstract spaces
34A37 Ordinary differential equations with impulses
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
45J05 Integro-ordinary differential equations
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References:

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