Abstract: | A minimal positive solution of the Thomas-Fermi problem ? = λt?1/2 w3/2, w(0) = 1, w(1) = w(1) is shown to exist for each λ > 0. It is proved that all positive solutions, for a given value of λ, are strictly ordered and that the minimal positive solution wλ is a decreasing function of λ. Upper and lower analytic bounds for w λ are given and these bounds are shown to initiate sequences of Picard and Newton iterates which converge monotonically to w λ. A comparative analysis of the efficiency of the iteration schemes is presented. The methods used are of a general nature and can be applied to a variety of nonlinear boundary value problems of convex type 14]. |