Nonautonomous impulsive systems with unbounded nonlinear terms

In Fenner and Pinto (1999) [23], proved that if the linear impulsive system satisfies the IS condition (see Definition 2.1) with bounded nonlinear term f ( t , x , ? ) , then the perturbed nonlinear impulsive system has a unique bounded solution (see Theorem A). The method used to prove Theorem A cannot be applied to the unbounded case. In this paper, we prove that if | f ( t , x , ? ) | ≤ µ e β | t | + M , then the perturbed nonlinear impulsive system has a unique solution.

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