On existence and uniqueness of $L_1$-solutions for quadratic integral equations via a Krasnoselskii-type fixed point theorem

Abstract

Using a Krasnoselskii-type fixed point theorem due to Burton, we discuss the existence of integrable solutions of general quadratic-Urysohn integral equations on a bounded interval $(a,b)$. Uniqueness of the solution is also studied. An example to illustrate our theory is also included.