On quadratic integral equations in Orlicz spaces

In this paper we study the quadratic integral equation of the form x ( t ) = g ( t ) + λ x ( t ) ∫ a b K ( t , s ) f ( s , x ( s ) ) d s . Several existence theorems for a.e. monotonic solutions in Orlicz spaces are proved for strongly nonlinear functions f. The presented method of the proof can be easily extended to different classes of solutions.