Chan, C. Y.; Hon, Y. C. A constructive solution for a generalized Thomas-Fermi theory of ionized atoms. (English) Zbl 0639.34021 Q. Appl. Math. 45, 591-599 (1987). This paper studies the problem: \(y''+(b/x)y'=cx^ py^ q,\) \(y(0)=1\), \(y(a)=0\), where b,c, and q are constants such that \(0\leq b<1\), \(c>0\), \(p>-2\) and \(q>1\). Modified Bessel functions of the first and the second kinds are used to construct Green’s function of a related linear problem, which is used in each successive approximation to the nonlinear problem. A sequence of lower bounds and a sequence of upper bounds are constructed explicitly such that each sequence converges to obtain existence of a nonnegative solution. Uniqueness follows from the maximum principle. The dependence of the solution on the size of the interval [0,a] is also established. To illustrate the computational method, two numerical examples, including the Thomas-Fermi model for the ionized atom, are given. Reviewer: C.Y.Chan Cited in 20 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65J99 Numerical analysis in abstract spaces Keywords:Bessel functions; Green’s function; maximum principle; computational method; numerical examples; Thomas-Fermi model for the ionized atom PDFBibTeX XMLCite \textit{C. Y. Chan} and \textit{Y. C. Hon}, Q. Appl. Math. 45, 591--599 (1987; Zbl 0639.34021) Full Text: DOI