A second-order impulsive Cauchy problem

Eduardo Hernández Morales

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-11

Abstract:

We study the existence of mild and classical solutions for an abstract second-order impulsive Cauchy problem modeled in the form u ¨ ( t ) = A u ( t ) + f ( t , u ( t ) , u ˙ ( t ) ) , t ∈ ( − T 0 , T 1 ) , t ≠ t i ; u ( 0 ) = x 0 , u ˙ ( 0 ) = y 0 ; △ u ( t i ) = I i 1 ( u ( t i ) ) . △ u ˙ ( t i ) = I i 2 ( u ˙ ( t i + ) ) where A is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space X and f , I i 1 , I i 2 are appropriate continuous functions.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:649632

DOI: 10.1155/S0161171202012735

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