Blow-up behavior of hammersteintype volterra integral equations

Hermann BRUNNER*, Z. W. Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

In this paper, we consider the blow-up behavior of Hammerstein-type Volterra integral equations. Based on several fundamental assumptions, some necessary and sufficient conditions under which the solution blows up in finite time are given. Some examples illustrate that there may always exist a global solution for a power-law function and that the blow-up behavior only depends upon the value of the kernel in a neighborhood of zero. As an application, we give some results on the blow-up behavior of Volterra integro-differential equations of Hammerstein-type.

Original languageEnglish
Pages (from-to)487-512
Number of pages26
JournalJournal of Integral Equations and Applications
Volume24
Issue number4
DOIs
Publication statusPublished - 2012

Scopus Subject Areas

  • Numerical Analysis
  • Applied Mathematics

User-Defined Keywords

  • Blow-up
  • Critical exponent
  • Volterra integral equations
  • Volterra integro-differential equations

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