Monotonic positive solution of a nonlinear quadratic functional integral equation

The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equation have been studied in 4], 5], 6], 7] and 8]. Here we are concerning with a nonlinear quadratic integral equation of Volterra type and we shall prove the existence of at least one L₁-positive monotonic solution for that equation under Carathèodory condition.