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

Dedicated to Professor Patrizia Pucci for her 65th birthday anniversary

• The existence of $L^{2}$-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.

Mathematics Subject Classification: Primary: 45G10, 47H10; Secondary: 47N20, 45B05, 45D05.

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