## Journal of Integral Equations and Applications

### On a nonlinear abstract Volterra equation

#### 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

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

#### 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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