Volterra functional equations via projective techniques

Oscillation of Volterra Integral Equations and Forced Functional Differential Equations

Regularity of Stochastic Volterra Equations by Functional Calculus Methods

We establish pathwise continuity properties of solutions to a stochastic Volterra equation with an additive noise term given by a local martingale. The deterministic part is governed by an operator with an H∞-calculus and a scalar kernel. The proof relies on the dilation theorem for positive definite operator families on a Hilbert space.

Theory and Numerical Analysis of Volterra Functional Equations

The qualitative and quantitative analyses of numerical methods delay differential equations (DDEs) are now quite well understood, as reflected in the recent monograph by Bellen and Zennaro (2003). This is in remarkable contrast to the situation in the numerical analysis of more general Volterra functional equations in which delays occur in connection with memory terms described by Volterra inte...

Volterra Functional Differential Equations: Existence, Uniqueness, and Continuation of Solutions

The initial-value problem for a class of Volterra functional differential equations— of sufficient generality to encompass, as special cases, ordinary differential equations, retarded differential equations, integro-differential equations, and hysteretic differential equations— is studied. A self-contained and elementary treatment of this over-arching problem is provided, in which a unifying th...

existence of solutions for a class of functional integral equations of volterra type in two variables via measure of noncompactness

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.