Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result

Abstract

The existence of \begin{document}$ L^{2} $\end{document} -nonnegative solutions for nonlinear quadratic integral equations on a bounded closed interval is investigated. Two existence results for different classes of functions are shown. As a consequence an existence theorem for the Chandrasekhar integral quadratic equation, well-known in theory of radiative transfer, is obtained. The aim is achieved by means of a new fixed point theorem for multimaps in locally convex linear topological spaces.