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

Yang, Zhanwen; Brunner, Hermann
April 2013
Frontiers of Mathematics in China;Apr2013, Vol. 8 Issue 2, p261
Academic Journal
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.


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