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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Blow-up behavior of Hammerstein-type delay Volterra integral equations

Language

English

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. © 2013 Higher Education Press and Springer-Verlag Berlin Heidelberg.

Keywords

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

Publication Date

2013

Source Publication Title

Frontiers Of Mathematics In China

Volume

8

Issue

2

Start Page

261

End Page

280

Publisher

Springer with Higher Education Press

ISSN (print)

16733452

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