scholarly journals On Hartree–Fock Systems

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 357-364
Author(s):  
I. Gasser
Keyword(s):  
Existence And Uniqueness ◽  
Semiclassical Limit ◽  
Uniqueness Result ◽  
Nonlinear Schrödinger ◽  
Hartree Fock ◽  
Self Consistent ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems

We show an existence and uniqueness result for mildly nonlinear Schrödinger systems of (self-consistent) Hartree–Fock form. We also shortly resume the already existing results on the semiclassical limit and the asymptotic and dispersive behavior of such systems.

Existence and uniqueness of positive solutions of nonlinear Schrödinger systems

2015 ◽  
Vol 145 (2) ◽  
pp. 365-390 ◽  
Author(s):  
Haidong Liu ◽  
Zhaoli Liu ◽  
Jinyong Chang
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Ground State ◽  
Existence And Uniqueness ◽  
Unique Positive Solution ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems ◽  
Least Energy ◽  
Schrödinger System

We prove that the Schrödinger systemwhere n = 1, 2, 3, N ≥ 2, λ1 = λ2 = … = λN = 1, βij = βji > 0 for i, j = 1, …, N, has a unique positive solution up to translation if the βij (i ≠ j) are comparatively large with respect to the βjj. The same conclusion holds if n = 1 and if the βij (i ≠ j) are comparatively small with respect to the βjj. Moreover, this solution is a ground state in the sense that it has the least energy among all non-zero solutions provided that the βij (i ≠ j) are comparatively large with respect to the βjj, and it has the least energy among all non-trivial solutions provided that n = 1 and the βij (i ≠ j) are comparatively small with respect to the βjj. In particular, these conclusions hold if βij = (i ≠ j) for some β and either β > max{β11, β22, …, βNN} or n = 1 and 0 < β < min{β11, β22, …, βNN}.

Compactness of Minimizing Sequences in Nonlinear Schrödinger Systems Under Multiconstraint Conditions

2014 ◽  
Vol 14 (1) ◽  
Author(s):  
Norihisa Ikoma
Keyword(s):  
Nonlinear Optics ◽  
Orbital Stability ◽  
Minimizing Sequences ◽  
Minimizing Sequence ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems ◽  
Schrödinger System

AbstractIn this paper, the precompactness of minimizing sequences under multiconstraint conditions are discussed. This minimizing problem is related to a coupled nonlinear Schrödinger system which appears in the field of nonlinear optics. As a consequence of the compactness of each minimizing sequence, the orbital stability of the set of all minimizers is obtained.

A Note on Nonlinear Schrödinger Systems: Existence of A-symmetric Solutions

2006 ◽  
Vol 6 (2) ◽  
Author(s):  
Antonio Ambrosetti
Keyword(s):  
Small Parameter ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems

AbstractThe paper contains some results concerning the existence of a-symmetric solutions to a class of autonomous nonlinear Schrödinger systems, coupled through a small parameter.

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