Frontiers of Mathematics in China >
Blow-up behavior of Hammerstein-type delay Volterra integral equations
Received date: 06 Apr 2012
Accepted date: 23 Aug 2012
Published date: 01 Apr 2013
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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.
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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