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 conside...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.展开更多
基金Acknowledgements The authors thank the anonymous referees for the constructive criticism and the many valuable suggestions that led to a significant improvement in the presentation of the main results. This work was supported by the National Natural Science Foundation of China （Grant No. 11071050）, the Fundamental Research Funds for the Central Universities （Grant No. HIT.NSRIF.2010051）, the Hong Kong Research Grants Council （RGC Project No. 200210）, and the Natural Sciences and Engineering Research Council of Canada （NSERC Discovery Grant A9406）.
文摘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.
