On a class of nonlinear integral equations of Urysohn's type

In this paper we study an interesting class of nonlinear integral equations of Urysohn's type, namely,

$\text{u(x) +}\text{∑}\text{j=l}\text{n}\text{∫}{}_{\mathrm{\Omega }}\text{k}{}_{\mathrm{j}}\text{(x,y)f}{}_{\mathrm{j}}\text{(y, u(y)) dy= v(x)}\text{(x ∈ Ω)}$

. It is shown that such an equation can be considered as a nonlinear operator equation of Hammerstein type in an appropriate Banach space. One can in this way extend the theory of nonlinear operator equations of Hammerstein type (except for the part which uses variational methods) to this class of equations.