Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrodinger operators

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Enstedt, M.²  Melgaard, M.¹ 

[1] Dublin Inst Technol, Sch Math Sci, Dublin 8, Ireland

[2] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

关键词: Nonlinear equations;    Hartree-Fock model;    Magnetic fields;    Excited states;    Ground state;    Critical point theory;   

DOI  :  10.1016/j.jde.2012.05.025

来源: Elsevier

【 摘 要 】

We consider a system of nonlinear coupled equations involving magnetic Schrodinger operators and general potentials. We provide the criteria for the existence of multiple solutions to these equations. As special cases we get the classical results on existence of infinitely many distinct solutions within Hartree and Hartree-Fock theory of atoms and molecules subject to an external magnetic fields. We also extend recent results within this theory, including Coulomb system with a constant magnetic field, a decreasing magnetic field and a physically measurable magnetic field. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free