Nonlinear Volterra equation with nondecreasing kernel
The author considers the following system of integral equations \[ x(t)= \int^t_0 k(t, s, x(s)) ds+ f(t), \qquad t\geq 0, \tag{1} \] where all functions are continuous in their domains and the kernel \(K(t, s, x)\) is a nondecreasing function of \(x\in \mathbb{R}^n\) (componentwise). By means of methods connected with integral inequalities existence and uniqueness theorems are proved for equation (1) and certain of its special cases.
scientific article; zbMATH DE number 898884