On Monotonic Integrable Solutions for Quadratic Functional Integral Equations

We study the solvability of functional quadratic integral equations in the space of integrable functions on the interval I = 0, 1]. We concentrate on a.e. monotonic solutions for considered problems. The existence result is obtained under the assumption that the functions involved in the investigated equation satisfy Carathéodory conditions. As a solution space we consider both L ₁(I) and L _p (I) spaces for p > 1.