A nonlinear elliptic system arising in electron density theory

Journal Article · Wed Jan 01 04:00:00 EST 1992 · Communications in Partial Differential Equations; (United States)

OSTI ID:7018074

Benilan, P ^[1]; Goldstein, J A ^[2]; Rieder, G R ^[3]

---

1. Universite de Besancon, Cedex (France)
2. MSRI, Berkeley, CA (United States) Tulane Univ., New Orleans, LA (United States) Louisiana State Univ., Baton Rouge (United States)
3. MSRI, Berkeley, CA (United States) Louisiana State Univ., Baton Rouge, LA (United States)

Of concern is the nonlinear system -[Delta]u[sub 1] + c[sub 1] (u[sub 1] - [lambda][sub 1])[sub +][sup 3/2] + c[sub 2] (u[sub 2] - [lambda][sub 2])[sub +][sup 3/2] = f[sub 1], -[Delta]u[sub 2] + c[sub 3] (u[sub 1] - [lambda][sub 1])[sub +][sup 3/2] c[sub 4] (u[sub 2] - [lambda][sub 2])[sub +][sup 3/2] = f[sub 2], in R[sup 3]. Here [lambda][sub i], c[sub j] are given positive constants. Such a system arises in spin polarized ground state electron density theory. The parameters [lambda][sub 1], [lambda][sub 2] should be such that N[sub 1] = c[sub 5] [integral] [sub R[sup 3]] (u[sub 1] - [lambda][sub 1])[sub +][sup 3/2] dx, N[sub 2] = c[sub 6] [integral][sub R[sup 3]] (a[sub 2] - [lambda][sub 2])[sub +][sup 3/2] dx where N[sub 1], N[sub 2] are given positive numbers satisfying N[sub 1] + N[sub 2] [le] Z + 1 where Z is some given positive number. (Here N[sub 1], N[sub 2], Z are, respectively, the number of spin up electrons, spin down electrons, and protons in the system). We establish existence for this problem. Uniqueness remains open. 7 refs.

• OSTI ID: 7018074
• Journal Information: Communications in Partial Differential Equations; (United States), Journal Name: Communications in Partial Differential Equations; (United States) Vol. 17:11-12; ISSN 0360-5302; ISSN CPDIDZ
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
664100 -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANALYTICAL SOLUTION
ANGULAR MOMENTUM
BARYONS
DIFFERENTIAL EQUATIONS
ELECTRON DENSITY
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
HADRONS
LEPTONS
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
NUCLEONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
PROTONS
SPIN