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چکیده
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In this paper, a constructive proof under some conditions is pre- sented for existence and uniqueness of the solutions to the sin- gular problem y ′′(x) − m x y(x) = f(x, y(x)), 0 < x ≤ 1, with the boundary conditions y(0) = 0, Ay(1) + By′ (1) = C. In general, f (x, y(x)) is assumed to be nonsingular with respect to the independent variable x but it is allowed be singular with respect to y and moreover, f (x, y(x)) can be sign changing as well. The Picard iterative sequence is then constructed based on integral equation with the help of positive Green’s function. The convergence of this iterative sequence is controlled by an adjustable parameter so that it converges to the unique solution in the - nite region in which ∂f ∂y is supposed to be nonnegative and bounded. Some examples also are given to demonstrate the trustworthiness of our constructive theory.
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