On generalized impulsive piecewise constant delay differential equations
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsiv...
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| Published in | Science China. Mathematics Vol. 58; no. 9; pp. 1981 - 2002 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Beijing
Science China Press
01.09.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-7283 1869-1862 |
| DOI | 10.1007/s11425-015-5010-8 |
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| Abstract | A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications. |
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| AbstractList | A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications. |
| Author | CHIU Kuo-Shou |
| AuthorAffiliation | Departamento de Matemdtica, Facultad de Ciencias Bdsicas, Universidad Metropolitana de Ciencias de la Educacidn, Josd Pedro Alessandri 774, Santiago, Chile |
| Author_xml | – sequence: 1 givenname: Kuo-Shou surname: Chiu fullname: Chiu, Kuo-Shou email: kschiu@umce.cl organization: Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación |
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| Cites_doi | 10.1006/jmaa.2001.7836 10.1016/j.amc.2009.03.071 10.1080/00036818508839568 10.14232/ejqtde.2013.1.49 10.1155/S0161171283000599 10.3846/1392-6292.2010.15.175-187 10.1016/0022-247X(92)90103-K 10.1007/s10440-009-9458-9 10.14232/ejqtde.2010.1.46 10.14232/ejqtde.2011.1.88 10.1090/S0002-9939-1987-0877038-7 10.1016/j.na.2009.02.131 10.1007/s10255-011-0107-5 10.1007/s10440-013-9863-y 10.1016/j.jmaa.2003.11.002 10.1016/0096-3003(87)90083-X 10.1016/0022-247X(84)90248-8 10.1080/10236198.2010.549003 10.1016/j.mcm.2008.10.001 10.1142/0906 10.1142/9789814343183 10.1090/S0002-9939-1987-0877047-8 10.1090/S0002-9939-1991-1057744-5 10.1016/B978-0-12-434170-8.50028-5 10.1142/2892 10.1142/1860 10.37193/CJM.2013.02.15 |
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| Keywords | 34A36 26D10 impulsive differential equation 34K34 34K45 Green function 34K11 34K20 oscillation Gronwall integral inequality piecewise constant delay of generalized type nonoscillation stability of solutions variation of parameters formula |
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| Notes | impulsive differential equation;piecewise constant delay of generalized type;variation of parameters formula;Gronwall integral i 11-5837/O1 A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| SubjectTerms | Applications of Mathematics Constants Delay Differential equations Inequalities Integrals Mathematical analysis Mathematics Mathematics and Statistics Oscillations Uniqueness theorems 分段线性 分片 唯一性定理 常微分方程 广义 积分不等式 脉冲微分方程 非线性时滞微分方程 |
| Title | On generalized impulsive piecewise constant delay differential equations |
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