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Existence results for first-order impulsive differential equations. (English) Zbl 0853.34011
With the help of a nonlinear Leray-Schauder type theorem the authors obtain some existence results for the impulsive initial value problem. They also study the periodic problem making use of upper and lower solutions. The results obtained complement those known in the literature.

MSC:
34A37 Ordinary differential equations with impulses
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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