Journal of Integral Equations and Applications

A multiple nonlinear Abel type integral equation

W. Mydlarczyk

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Abstract

We discuss a multiple nonlinear Abel type integral equation. The basic results provide criteria for the existence of nontrivial everywhere positive solutions. They are expressed in terms of the generalized Osgood condition. The global behavior of the solution, especially the conditions when it experiences blow-up, is also considered.

Article information

Source
J. Integral Equations Applications, Volume 27, Number 4 (2015), 555-572.

Dates
First available in Project Euclid: 8 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1454939253

Digital Object Identifier
doi:10.1216/JIE-2015-27-4-555

Mathematical Reviews number (MathSciNet)
MR3457682

Zentralblatt MATH identifier
1334.45005

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12]
Secondary: 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 45G05: Singular nonlinear integral equations 45G10: Other nonlinear integral equations

Keywords
Nonlinear Abel type integral equations the existence and uniqueness of solutions to integral Volterra equations nontrivial solutions the maximal solution blow-up solutions

Citation

Mydlarczyk, W. A multiple nonlinear Abel type integral equation. J. Integral Equations Applications 27 (2015), no. 4, 555--572. doi:10.1216/JIE-2015-27-4-555. https://projecteuclid.org/euclid.jiea/1454939253


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