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Blow-up behavior of Hammerstein-type delay Volterra integral equations |
Zhanwen YANG1( ), Hermann BRUNNER2 |
| 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 |
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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.
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| Keywords
Delay Volterra integral equation (DVIE)
non-vanishing delay
vanishing delay
blow-up of solution
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Corresponding Author(s):
YANG Zhanwen,Email:yangzhan_wen@126.com
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Issue Date: 01 April 2013
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