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

作者：Enstedt M; Melgaard M^*

来源：Journal of Differential Equations, 2012, 253(6): 1729-1743.

DOI：10.1016/j.jde.2012.05.025

• Nonlinear equations
• Hartree-Fock model
• Magnetic fields
• Excited states
• Ground state
• Critical point theory

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 %26quot;physically measurable%26quot; magnetic field.

• 出版日期2012-9-15