Thomas-Fermi方程的边值问题

Boundary Value Problems for Thomas-Fermi Equation

本文利用上下解和隐函数定理等技巧,研究了奇异方程ψ(t)x″=f(t,x,x′)和ψ(t)x″=f(t,x)的某些边值问题解的存在唯一性,证明了Thomas-Fermi方程对应于正离子型和具有Bohr半径b的中性原子型的边值问题有唯一解,并给出了前一问题解的界估计。

In this paper, making use of upper and lower solutions and implicit function technique, we study the solvability and the uniqueness of spome boundary value problems for singular equations Ψ(t)x″=f(t,x,x′) and Ψ(t)x″=f(t,x), prove that the first and the third boundary value problems of Thomas-Fermi equation have unique solutions respectively, give the bounded estimate of solution for the first boundary value problem with Thomas-Fermi equation.