Nonconvolution nonlinear integral volterra equations with monotone operators

Qualitative Properties of Nonlinear Volterra Integral Equations

In this article, the contraction mapping principle and Liapunov’s method are used to study qualitative properties of nonlinear Volterra equations of the form x(t) = a(t)− ∫ t 0 C(t, s)g(s, x(s)) ds, t ≥ 0. In particular, the existence of bounded solutions and solutions with various L properties are studied under suitable conditions on the functions involved with this equation.

Some Problems in Nonlinear Volterra Integral Equations

Upper and lower bounds for the norm of solutions of systems of first order differential equations as well as theorems on global existence and boundedness and other useful results have recently been obtained by comparing solutions of the given system with those of a related (single) first order differential equation. This technique, which is essentially due to Conti [5] and Wintner [9], has been...

Exact solutions of nonlinear interval Volterra integral equations

A computational method for nonlinear mixed Volterra-Fredholm integral equations

In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.    

An Iterative Scheme for Solving Nonlinear Equations with Monotone Operators

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with monotone operators is proposed and its convergence is proved. A discrepancy principle is proposed and justified. A priori and a posterior...