Journal of Integral Equations and Applications

On a nonlinear abstract Volterra equation

Etienne Emmrich and Guy Vallet

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Abstract

Existence of solutions is shown for equations of the type $Av + B( KGv,v) = f$, where $A$, $B$ and $G$ are possibly nonlinear operators acting on a Banach space $V$, and $K$ is a Volterra operator of convolution type. The proof relies on the convergence of a suitable time discretization scheme.

Article information

Source
J. Integral Equations Applications, Volume 28, Number 1 (2016), 75-89.

Dates
First available in Project Euclid: 15 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1460727505

Digital Object Identifier
doi:10.1216/JIE-2016-28-1-75

Mathematical Reviews number (MathSciNet)
MR3488155

Zentralblatt MATH identifier
1334.45004

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12] 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25] 65J08: Abstract evolution equations

Keywords
Nonlinear Volterra equation time discretization existence

Citation

Emmrich, Etienne; Vallet, Guy. On a nonlinear abstract Volterra equation. J. Integral Equations Applications 28 (2016), no. 1, 75--89. doi:10.1216/JIE-2016-28-1-75. https://projecteuclid.org/euclid.jiea/1460727505


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