## Abstract

We study a class of generalized differential equations with the following features: 1) a typical equation from this class is driven by a measure on the given time-interval; this measure may be the ordinary Lebesgue measure, but it also may be a jump measure, another Borel or even a random measure; 2) the right-hand side of the equation depends on the differential of the solution, 3) the equation admits time-delays, 4) the equation is linear. Our interest in this class of differential equations is motivated by applications in the theories of impulsive, random and hereditary systems as well as in the control theory. This paper treats essentially existence, uniqueness and representation of solutions, but we also give many examples. The paper is supposed to be followed by some more papers we are working on now.

Original language | English |
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Pages (from-to) | 615-638 |

Number of pages | 24 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms |

Volume | 6 |

Issue number | 4 |

State | Published - 1 Dec 1999 |

Externally published | Yes |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics