A second-order impulsive Cauchy problem

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∈(−T0,T1),t≠ti;u(0)=x0,u˙(0)=y0; △u(ti)=Ii1 (u (ti)). △u˙(ti)=Ii2 (u˙ (ti+)) where A is the infinitesimal generator of a strongly continuous...

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Main Author: Eduardo Hernández Morales
Format: Article
Language:English
Published: Wiley 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202012735
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author Eduardo Hernández Morales
author_facet Eduardo Hernández Morales
author_sort Eduardo Hernández Morales
collection DOAJ
description 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∈(−T0,T1),t≠ti;u(0)=x0,u˙(0)=y0; △u(ti)=Ii1 (u (ti)). △u˙(ti)=Ii2 (u˙ (ti+)) where A is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space X and f,Ii1, Ii2 are appropriate continuous functions.
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spelling doaj-art-d1ca06a75ebf422f98cedefc317e095e2025-08-20T03:23:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131845146110.1155/S0161171202012735A second-order impulsive Cauchy problemEduardo Hernández Morales0Departamento de Matemática, Instituto de Ciências Matemáticas de São Carlos, Universidade de São Paulo, Caixa Postal 668, São Carlos 13560-970, São Paulo, BrazilWe 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∈(−T0,T1),t≠ti;u(0)=x0,u˙(0)=y0; △u(ti)=Ii1 (u (ti)). △u˙(ti)=Ii2 (u˙ (ti+)) where A is the infinitesimal generator of a strongly continuous cosine family of linear operators on a Banach space X and f,Ii1, Ii2 are appropriate continuous functions.http://dx.doi.org/10.1155/S0161171202012735
spellingShingle Eduardo Hernández Morales
A second-order impulsive Cauchy problem
International Journal of Mathematics and Mathematical Sciences
title A second-order impulsive Cauchy problem
title_full A second-order impulsive Cauchy problem
title_fullStr A second-order impulsive Cauchy problem
title_full_unstemmed A second-order impulsive Cauchy problem
title_short A second-order impulsive Cauchy problem
title_sort second order impulsive cauchy problem
url http://dx.doi.org/10.1155/S0161171202012735
work_keys_str_mv AT eduardohernandezmorales asecondorderimpulsivecauchyproblem
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