On a class of Urysohn–Stieltjes quadratic integral equations and their applications

We investigate a class of nonlinear quadratic integral equation of Urysohn–Stieltjes type. Such a class contains a number of classical nonlinear quadratic integral equations such as the Chandrasekhar quadratic integral equation. We consider the solvability of the equations in question in the space of continuous functions under very general assumptions. Several particular cases of the assumed hypotheses are discussed and numerous applications are indicated.