Differential and Integral Equations

An application of a diffeomorphism theorem to Volterra integral operator

Josef Diblík, Marek Galewski, Marcin Koniorczyk, and Ewa Schmeidel

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1526004033

Mathematical Reviews number (MathSciNet)
MR3801827

Zentralblatt MATH identifier
06890407

Subjects
Primary: 26B10: Implicit function theorems, Jacobians, transformations with several variables 47J07: Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]

Citation

Diblík, Josef; Galewski, Marek; Koniorczyk, Marcin; Schmeidel, Ewa. An application of a diffeomorphism theorem to Volterra integral operator. Differential Integral Equations 31 (2018), no. 7/8, 621--642. https://projecteuclid.org/euclid.die/1526004033


Export citation