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

Zhanwen Yang*, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)261-280
Number of pages20
JournalFrontiers of Mathematics in China
Volume8
Issue number2
DOIs
Publication statusPublished - Apr 2013

Scopus Subject Areas

  • Mathematics (miscellaneous)

User-Defined Keywords

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

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