|ON MONOTONIC SOLUTIONS OF A SINGULAR QUADRATIC INTEGRAL EQUATION WITH SUPREMUM
|Year of Publication
|Dynamic Systems and Applications
|AMS Subject Classification
|45G10, 45M99, 47H09
We prove an existence theorem for a singular quadratic integral equation with supremum. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equations with supremum has a monotonic solution in C[0, 1]. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.