Abstract Criteria for Multiple Solutions to Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators

Mattias Enstedt
Michael Melgaard

Journal of Differential Equations, Volume 253, no. 6, 15 September 2012, Pages 1729-1743


We consider a system of nonlinear coupled equations involving magnetic Schrodinger

operators and general potentials. We provide a criteria for the existence of multiple

solutions to these equations. As special cases we get the classical results on

existence of innitely 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.