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

DOI10.1016/j.jde.2012.05.025zbMath1248.35167OpenAlexW1997003998MaRDI QIDQ441224

Michael Melgaard, Mattias Enstedt

Publication date: 20 August 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2012.05.025

zbMATH Keywords

magnetic fieldsground statecritical point theorynonlinear equationsexcited statesHartree-Fock model

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Molecular physics (81V55)

Related Items

The compatible Grassmannian

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stiefel and Grassmann manifolds in quantum chemistry
• Existence of a solution to Hartree-Fock equations with decreasing magnetic fields
• Non-existence of a minimizer to the magnetic Hartree-Fock functional
• Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations
• Second order information of Palais-Smale sequences in the mountain pass theorem
• Remarks on Schrödinger operators with vector potentials
• Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations
• Solutions of Hartree-Fock equations for Coulomb systems
• Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds
• On the existence of entire solutions to a class of semilinear elliptic equations on noncompact Riemannian manifolds
• Finite Morse index solutions of exponential problems
• NON-RADIALLY SYMMETRIC SOLUTIONS FOR A SUPERLINEAR AMBROSETTI–PRODI TYPE PROBLEM IN A BALL
• A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
• Nontrivial solutions of operator equations and Morse indices of critical points of min-max type
• Morse indices at critical points related to the symmetric mountain pass theorem and applications
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• Morse‐type information on palais‐smale sequences obtained by min‐max principles
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• Schrödinger operators with singular magnetic vector potentials
• Higher energy solutions in the theory of phase transitions: A variational approach

This page was built for publication: Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators