American Institute of Mathematical Sciences

July  2020, 13(7): 1947-1955. doi: 10.3934/dcdss.2020152

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

 Department of Mathematics and Computer Science, University of Perugia, Perugia, 060123, Italy

Dedicated to Professor Patrizia Pucci for her 65th birthday anniversary

Received  September 2018 Revised  October 2018 Published  November 2019

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.

Citation: Tiziana Cardinali, Paola Rubbioni. Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result. Discrete & Continuous Dynamical Systems - S, 2020, 13 (7) : 1947-1955. doi: 10.3934/dcdss.2020152
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