Abstract
ABSTRACTIn this paper, a constructive proof under some conditions is presented for existence and uniqueness of the solutions to the singular problem with the boundary conditionsIn 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 finite region in which is supposed to be nonnegative and bounded. Some examples also are given to demonstrate the trustworthiness of our constructive theory.
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