Almost sure stability of linear Itô-Volterra equations with damped stochastic perturbations.
An abstract inverse problem.
An abstract nonlinear second order differential equation
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel
Mathematics Subject Classification: 44A40, 45B05The paper presents an abstract linear second kind Fredholm integral equation with degenerated kernel defined by means of the Bittner operational calculus. Fredholm alternative for mutually conjugated integral equations is also shown here. Some examples of solutions of the considered integral equation in various operational calculus models are also given.
An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally...
An Adaptive Numerical Method for Solving Linear Fredholm Integral Equations of the First Kind.
An algebra of integral operators.
An algebraic derivative associated to the operator
In this paper we get an algebraic derivative relative to the convolution associated to the operator , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation
An Analysis of the Numerical Solution of Fredholm Integral Equations of the First Kind.
An application of Markov operators in differential and integral equations
An approximate solution of some Volterra integral equation with a smooth kernel
The behaviour near the origin of nontrivial solutions to integral Volterra equations with a power nonlinearity is studied. Estimates of nontrivial solutions are given and some numerical examples are considered.
An asymptotic expansion of the solution to a system of integrodifferential equations with exact asymptotics for the remainder.
An continuation results for Fredholm integral equations on locally convex spaces.
An effective method for solving fractional integro-differential equations.
An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective
A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected...
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.
An existence theorem for an implicit integral equation with discontinuous right-hand side.
An existence theorem for Hammerstein integral equations.
An existence theorem for semilinear functional parabolic equations