Open Access
2016 On a nonlinear abstract Volterra equation
Etienne Emmrich, Guy Vallet
J. Integral Equations Applications 28(1): 75-89 (2016). DOI: 10.1216/JIE-2016-28-1-75


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.


Download Citation

Etienne Emmrich. Guy Vallet. "On a nonlinear abstract Volterra equation." J. Integral Equations Applications 28 (1) 75 - 89, 2016.


Published: 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1334.45004
MathSciNet: MR3488155
Digital Object Identifier: 10.1216/JIE-2016-28-1-75

Primary: 45D05 , 47J35 , 65J08

Keywords: existence , Nonlinear Volterra equation , time discretization

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.28 • No. 1 • 2016
Back to Top