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

Tiziana Cardinali; Paola Rubbioni

doi:10.3934/dcdss.2020152

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2020, Volume 13, Issue 7: 1947-1955. Doi: 10.3934/dcdss.2020152

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

Tiziana Cardinali and
Paola Rubbioni

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

Dedicated to Professor Patrizia Pucci for her 65th birthday anniversary

Received: August 31, 2018

Revised: September 30, 2018

Published: April 2020

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Abstract

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.

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

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