Nonlinear Volterra integral equations with positive definite kernels

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

collocation method for fredholm-volterra integral equations with weakly kernels

in this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎fredholm-volterra integral equations (fvies) are smooth‎.

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