The generalized Thomas–Fermi singular boundary value problems for neutral atoms

Abstract

SUMMARYThis paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas-Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive su cient conditions for the existenceconstruction of the above-mentioned upper-lower solutions.

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“…A singular boundary value problem occurs when a differential equation in a boundary value problem has a singular point at one boundary 1 . Such problems frequently arise in areas such as thermal explosions, electrohydrodynamics, chemical reactions, and atomic and nuclear physics [2][3][4] . Russell and Shampine 5 have discussed a classical three-point finite difference scheme for solving singular boundary value problems which gives good approximation solutions with a moderate step size.…”

Some regularity results to the generalized Emden–Fowler equation with irregular data

“…A necessary and sufficient condition on g for the existence of solutions to with θ > 0 was given by Taliaferro , who also proved that such solutions are unique. For a deeper discussion, see , and for results regarding more general equations, see .…”

Positive Solutions for a Class of Singular Two Point Boundary Value Problems

“…Singular boundary value problems arise in various fields of Mathematics and Physics such as nuclear physics, boundary layer theory, nonlinear optics, gas dynamics, etc, [1,5,9,12,14,17,18,19]. For more details on singular BVPs and recent developments, we refer the readers to the recent monograph by R. P. Agarwal and D. O' Regan [4] and [6,8,9,15].…”