Complementary variational principles for ∇2φ = f(φ) with applications to the Thomas–Fermi and Liouville equations-Reference-Cited by-同舟云学术

Complementary variational principles for ∇2φ = f(φ) with applications to the Thomas–Fermi and Liouville equations

Published:1969-03 Issue:2 Volume:65 Page:535-541
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Arthurs A. M.,Robinson P. D.

Abstract

AbstractComplementary variational principles associated with the boundary-value problem ∇2φ = f(φ) in ∇,φ = φ0 on the boundary of ∇, are presented. The theory is applied to the Thomas–Fermi equation in quantum mechanics and the Liouville equation in equilibrium statistical mechanics.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference7 articles.

1. Complementary variational principles in perturbation theory

2. Complementary variational principles for a generalized diffusion equation

3. (1) Noble B. University of Wisconsin, Mathematics Research Center, Report no. 473 (1964).

Cited by 18 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Oscillation Criteria of Two-Dimensional Time-Scale Systems;Oscillators - Recent Developments;2019-06-26

2. Macromolecular electrostatic energy within the nonlinear Poisson–Boltzmann equation;The Journal of Chemical Physics;1994-02-15

3. On optimization procedures based upon the atomic thomas-fermi energy;International Journal of Quantum Chemistry;1986-06

4. Complementary variational principle for density-functional theories;Physical Review A;1983-01-01

5. Variational analysis of a perturbed free boundary problem;Communications in Partial Differential Equations;1982-01