## Differential and Integral Equations

### An application of a diffeomorphism theorem to Volterra integral operator

#### Abstract

Using global diffeomorphism theorem based on duality mapping and mountain geometry, we investigate the properties of the Volterra operator given pointwise for $t\in \left[ 0,1\right]$ by \begin{equation*} V(x)(t)=x(t)+ \int _{0}^{t} v(t,\tau ,x(\tau ))d\tau ,\text{ }x(0)=0. \end{equation*}

#### Article information

Source
Differential Integral Equations, Volume 31, Number 7/8 (2018), 621-642.

Dates
First available in Project Euclid: 11 May 2018