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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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202012735 |
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| _version_ | 1849683120575479808 |
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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. |
| format | Article |
| id | doaj-art-d1ca06a75ebf422f98cedefc317e095e |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| 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 AT eduardohernandezmorales secondorderimpulsivecauchyproblem |