A Liouville's theorem for a fractional elliptic system with indefinite nonlinearities

2020 ◽  
Vol 492 (2) ◽  
pp. 124471
Author(s):  
Qiuping Geng ◽  
Jun Wang
Keyword(s):  
Elliptic System ◽  
Indefinite Nonlinearities ◽  
Liouville’S Theorem

scholarly journals Liouville's theorem for a fractional elliptic system

2019 ◽  
Vol 39 (3) ◽  
pp. 1545-1558
Author(s):  
Pengyan Wang ◽  
◽  
Pengcheng Niu
Keyword(s):  
Elliptic System ◽  
Liouville’S Theorem

DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

1999 ◽  
Vol 13 (02) ◽  
pp. 161-189
Author(s):  
C. SYROS
Keyword(s):  
Quantum Mechanics ◽  
Radiation Spectrum ◽  
Black Body ◽  
Boltzmann Distribution ◽  
Black Body Radiation ◽  
Planck Constant ◽  
Klein Gordon ◽  
Energy Variable ◽  
Liouville’S Theorem ◽  
Liouville’S Equation

The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation. Reality and additivity of F(g): (i) quantize the time variable; (ii) quantize the energy variable; (iii) quantize the Maxwell–Boltzmann distribution; (iv) make F(g) observable through time-elimination; (v) produce the Planck constant; (vi) yield the black-body radiation spectrum; (vii) support chronotopology introduced axiomatically; (viii) the Schrödinger and the Klein–Gordon equations follow. Hence, quantum theory appears as a corollary of Liouville's theorem. An unknown connection is found allowing the better understanding of space-times and of these theories.

On Some Generalized Compound Problem for a Nonlinear Elliptic System

1986 ◽  
Vol 126 (1) ◽  
pp. 55-62
Author(s):  
J. Wolska-Bochenek ◽  
L. Von Wolfersdorf
Keyword(s):  
Elliptic System ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic
Sign in / Sign up

Export Citation Format

Share Document