Department of Mathematics
Blow-up behavior of Hammerstein-type delay Volterra integral equations
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. © 2013 Higher Education Press and Springer-Verlag Berlin Heidelberg.
blow-up of solution, Delay Volterra integral equation (DVIE), non-vanishing delay, vanishing delay
Source Publication Title
Frontiers Of Mathematics In China
Springer with Higher Education Press
Yang, Zhanwen, and Hermann Brunner. "Blow-up behavior of Hammerstein-type delay Volterra integral equations." Frontiers Of Mathematics In China 8.2 (2013): 261-280.