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

Zhanwen Yang; Hermann BRUNNER

doi:10.1007/s11464-013-0293-y

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

Zhanwen Yang^*, Hermann BRUNNER

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

13 Citations (Scopus)

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. 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.

Original language	English
Pages (from-to)	261-280
Number of pages	20
Journal	Frontiers of Mathematics in China
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s11464-013-0293-y
Publication status	Published - Apr 2013

Scopus Subject Areas

Mathematics (miscellaneous)

User-Defined Keywords

blow-up of solution
Delay Volterra integral equation (DVIE)
non-vanishing delay
vanishing delay

Access to Document

10.1007/s11464-013-0293-y

Cite this

@article{72dc7ecdf41b4269a0270ea0f6755fd6,

title = "Blow-up behavior of Hammerstein-type delay Volterra integral equations",

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. 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.",

keywords = "blow-up of solution, Delay Volterra integral equation (DVIE), non-vanishing delay, vanishing delay",

author = "Zhanwen Yang and Hermann BRUNNER",

note = "Funding Information: 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).",

year = "2013",

month = apr,

doi = "10.1007/s11464-013-0293-y",

language = "English",

volume = "8",

pages = "261--280",

journal = "Frontiers of Mathematics in China",

issn = "1673-3452",

publisher = "Higher Education Press",

number = "2",

}

TY - JOUR

T1 - Blow-up behavior of Hammerstein-type delay Volterra integral equations

AU - Yang, Zhanwen

AU - BRUNNER, Hermann

N1 - Funding Information: 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).

PY - 2013/4

Y1 - 2013/4

N2 - 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.

AB - 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.

KW - blow-up of solution

KW - Delay Volterra integral equation (DVIE)

KW - non-vanishing delay

KW - vanishing delay

UR - http://www.scopus.com/inward/record.url?scp=84875513705&partnerID=8YFLogxK

U2 - 10.1007/s11464-013-0293-y

DO - 10.1007/s11464-013-0293-y

M3 - Journal article

AN - SCOPUS:84875513705

SN - 1673-3452

VL - 8

SP - 261

EP - 280

JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

IS - 2

ER -

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

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this