Differential and Integral Equations

An application of a diffeomorphism theorem to Volterra integral operator

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

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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

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

First available in Project Euclid: 11 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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