Blow-up behavior of hammersteintype volterra integral equations

H. Brunner; Z. W. Yang

doi:10.1216/JIE-2012-24-4-487

Blow-up behavior of hammersteintype volterra integral equations

H. Brunner^*, Z. W. Yang

^*Corresponding author for this work

Department of Mathematics

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

20 Citations (Scopus)

Abstract

In this paper, we consider the blow-up behavior of Hammerstein-type Volterra integral equations. Based on several fundamental assumptions, some necessary and sufficient conditions under which the solution blows up in finite time are given. Some examples illustrate that there may always exist a global solution for a power-law function and that the blow-up behavior only depends upon the value of the kernel in a neighborhood of zero. As an application, we give some results on the blow-up behavior of Volterra integro-differential equations of Hammerstein-type.

Original language	English
Pages (from-to)	487-512
Number of pages	26
Journal	Journal of Integral Equations and Applications
Volume	24
Issue number	4
DOIs	https://doi.org/10.1216/JIE-2012-24-4-487
Publication status	Published - 2012

Scopus Subject Areas

Numerical Analysis
Applied Mathematics

User-Defined Keywords

Blow-up
Critical exponent
Volterra integral equations
Volterra integro-differential equations

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10.1216/JIE-2012-24-4-487

Cite this

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title = "Blow-up behavior of hammersteintype volterra integral equations",

abstract = "In this paper, we consider the blow-up behavior of Hammerstein-type Volterra integral equations. Based on several fundamental assumptions, some necessary and sufficient conditions under which the solution blows up in finite time are given. Some examples illustrate that there may always exist a global solution for a power-law function and that the blow-up behavior only depends upon the value of the kernel in a neighborhood of zero. As an application, we give some results on the blow-up behavior of Volterra integro-differential equations of Hammerstein-type.",

keywords = "Blow-up, Critical exponent, Volterra integral equations, Volterra integro-differential equations",

author = "H. Brunner and Yang, {Z. W.}",

note = "The research leading to this paper has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant A9406), the Hong Kong Research Grants Council (RGC Project No. 200210), the National Natural Science Foundation of China (11071050), and the Fundamental Research Funds for the Central Universities (Grant No. HIT.NSRIF.2010051).",

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AU - Brunner, H.

AU - Yang, Z. W.

N1 - The research leading to this paper has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant A9406), the Hong Kong Research Grants Council (RGC Project No. 200210), the National Natural Science Foundation of China (11071050), and the Fundamental Research Funds for the Central Universities (Grant No. HIT.NSRIF.2010051).

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N2 - In this paper, we consider the blow-up behavior of Hammerstein-type Volterra integral equations. Based on several fundamental assumptions, some necessary and sufficient conditions under which the solution blows up in finite time are given. Some examples illustrate that there may always exist a global solution for a power-law function and that the blow-up behavior only depends upon the value of the kernel in a neighborhood of zero. As an application, we give some results on the blow-up behavior of Volterra integro-differential equations of Hammerstein-type.

AB - In this paper, we consider the blow-up behavior of Hammerstein-type Volterra integral equations. Based on several fundamental assumptions, some necessary and sufficient conditions under which the solution blows up in finite time are given. Some examples illustrate that there may always exist a global solution for a power-law function and that the blow-up behavior only depends upon the value of the kernel in a neighborhood of zero. As an application, we give some results on the blow-up behavior of Volterra integro-differential equations of Hammerstein-type.

KW - Blow-up

KW - Critical exponent

KW - Volterra integral equations

KW - Volterra integro-differential equations

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DO - 10.1216/JIE-2012-24-4-487

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VL - 24

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JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

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ER -

Blow-up behavior of hammersteintype volterra integral equations

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