Singular non-linear two-point boundary value problems: Existence and uniqueness

Abstract: A general approach is presented for proving existence and uniqueness of solutions to the singular boundary value problem The proof is constructive in nature, and could be used for numerical generation of the solution. The only restriction placed on is that it not be a singular function of the independent variable ; singularities in are easily avoided. Solutions are found in finite regions where , using an integral equation whose Green’s function contains an adjustable parameter that secures convergence of the Picard iterative sequence. Methods based on the theory are developed and applied to a set of problems that have appeared previously in published works. [Copyright &y& Elsevier]