Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 2: 261 - 280

DOI: https://doi.org/10.1007/s11464-013-0293-y

REVIEW ARTICLE

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

  • Zhanwen YANG , 1 ,
  • Hermann BRUNNER 2
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  • 1. Science Research Center, Academy of Fundamental and Interdisciplinary Science; Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
  • 2. Department of Mathematics, Hong Kong Baptist University, Hong Kong SAR, China; Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 557, Canada

Received date: 06 Apr 2012

Accepted date: 23 Aug 2012

Published date: 01 Apr 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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. he blow-up behaviors of DVIEs with non-vanishing delay vary with different nitial functions and the length of the lag, while DVIEs with pantograph delay wn the same blow-up behavior of VIEs. Some examples and applications to elay differential equations illustrate this influence.

Key words： Delay Volterra integral equation (DVIE); non-vanishing delay; vanishing delay; blow-up of solution

Cite this article

Zhanwen YANG , Hermann BRUNNER . Blow-up behavior of Hammerstein-type delay Volterra integral equations[J]. Frontiers of Mathematics in China, 2013 , 8(2) : 261 -280 . DOI: 10.1007/s11464-013-0293-y

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