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Utilizzando una generalizzazione della disuguaglianza di Gronwall si fornisce una stima puntuale per la soluzione dell’equazione lineare integrale di Volterra di seconda specie. Tale stima può essere applicata utilmente anche nello studio della stabilità di equazioni di evoluzione per mezzi continui.

A silent-noisy versus silent duel

A. Styszyński (1980)

Applicationes Mathematicae

A singular initial value problem for the equation $u^{(n)} (x) = g (u (x))$

Wojciech Mydlarczyk (1998)

Annales Polonici Mathematici

We consider the problem of the existence of positive solutions u to the problem $u^{(n)} (x) = g (u (x))$ , $u (0) = u^{'} (0) = . . . = u^{(n - 1)} (0) = 0$ (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition $\int ₀^{δ} 1 / s {[s / g (s)]}^{1 / n} d s < \infty$ is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.

$A$ -stable methods of high order for Volterra integral equations

Ľubor Malina (1975)

Aplikace matematiky

Method for numerical solution of Volterra integral equations, based on the O.I.M. methods, is suggested. It is known that the class of O.I.M. methods includes $A$ -stable methods of arbitrary high order of asymptotic accuracy. In part 5, it is proved that these methods generate methods for numerical solution of Volterra equations which are also $A$ -stable and of an arbitrarily high order. There is one advantage of the methods. Namely, they need no matrix inversion in the course of their numerical realization....

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A generalization of Constantin's integral inequality and its discrete analogue.

A Liapunov functional for a linear integral equation.

A method for solving the Volterra integral equation of the first kind

A mixed game of timing: problem of optimality

A note on controllability of nonlinear Volterra integrodifferential systems

A note on nonlinear integral equations

A note on the stability of $θ$ -methods for Volterra integral equations of the second kind

A note on Volterra integral equations with degenerate kernel

A pointwise estimate for the solution to a linear Volterra integral equation

A silent-noisy versus silent duel

A singular initial value problem for the equation $u^{(n)} (x) = g (u (x))$

$A$ -stable methods of high order for Volterra integral equations

A two-dimensional inverse heat conduction problem for estimating heat source.

A Volterra inequality with the power type nonlinear kernel.

Addendum to “Integrable and continuous solutions of a nonlinear quadratic integral equation”.

Algèbres de Volterra de certains espaces affines symétriques

Almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay.

Almost sure stability of linear Itô-Volterra equations with damped stochastic perturbations.

An existence result of asymptotically stable solutions for an integral equation of mixed type.

An existence theorem for a Volterra integral equation with deviating arguments.

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