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<p/> <p>This paper deals with the existence and iteration of positive solutions for the following one-dimensional <inline-formula> <graphic file="1687-2770-2008-860414-i2.gif"/></inline-formula>-Laplacian boundary value problems: <inline-formula> <graphic file="1687-2770-2008-860414-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-860414-i4.gif"/></inline-formula>, subject to some boundary conditions. By making use of monotone iterative technique, not only we obtain the existence of positive solutions for the problems, but also we establish iterative schemes for approximating the solutions.</p>