## Abstract

We consider the blow-up behavior of Hammerstein-type delay Volterra integral equations (DVIEs). Two types of delays, i. e., vanishing delay (pantograph delay) and non-vanishing delay (constant delay), are considered. With the same assumptions of Volterra integral equations (VIEs), in a similar technology to VIEs, the blow-up conditions of the two types of DVIEs are given. The blow-up behaviors of DVIEs with non-vanishing delay vary with different initial functions and the length of the lag, while DVIEs with pantograph delay own the same blow-up behavior of VIEs. Some examples and applications to delay differential equations illustrate this influence.

Original language | English |
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Pages (from-to) | 261-280 |

Number of pages | 20 |

Journal | Frontiers of Mathematics in China |

Volume | 8 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2013 |

## Scopus Subject Areas

- Mathematics (miscellaneous)

## User-Defined Keywords

- blow-up of solution
- Delay Volterra integral equation (DVIE)
- non-vanishing delay
- vanishing delay