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All functions appearing here are nonnegative and defined for 0 6 y< x. Equation (1) has the trivial solution U (X) z 0. It can have also other solutions. We prove, using the method due to Okrasinski, that under certain conditions upon a (x, y) and d (x) there can be at most one solution which does not vanish identically in a neighborhood of 0. Our main result is the attraction property of this nonnegative solution, provided that it exists. Namely we show that the iterations T" u of the operator