A multiplicity result for singular NLS equations with magnetic potentials

DOI10.1016/j.na.2007.03.044zbMath1159.35423OpenAlexW2038992449MaRDI QIDQ943770

Sara Barile

Publication date: 10 September 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.03.044

zbMATH Keywords

external magnetic fieldsemiclassical limitnonlinear Schrödinger equationssingular potentialsLjusternik-Schnirelman category

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Variational methods for second-order elliptic equations (35J20)

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Existence and concentration behavior of ground state solutions for magnetic nonlinear Choquard equations ⋮ The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field ⋮ New critical point theorem and infinitely many small-magnitude solutions of a nonlinear Iwatsuka model ⋮ Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities ⋮ On the fractional Schrödinger equations with critical nonlinearity ⋮ Least energy solutions for semilinear Schrödinger equation with electromagnetic fields and critical growth ⋮ Properties of ground states of nonlinear Schrödinger equations under a weak constant magnetic field ⋮ A new critical point theorem and small magnitude solutions of magnetic Schrödinger equations with Landau levels ⋮ Existence results for nonlinear Schrödinger systems with electromagnetic fields in ℝ^N ⋮ Multiplicity of semiclassical solutions to nonlinear Schrödinger equations ⋮ An existence result for a class of magnetic problems in exterior domains ⋮ Concentrating solutions for a magnetic Schrödinger equation with critical growth ⋮ Semiclassical solutions for a class of Schrödinger system with magnetic potentials ⋮ Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field

Cites Work

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• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• On multi-bump semi-classical bound states of nonlinear Schrödinger equations with electromagnetic fields
• Single-peaks for a magnetic Schrödinger equation with critical growth
• Critical point theory and Hamiltonian systems
• Schrödinger operators with magnetic fields. I: General interactions
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
• Semi-classical states for nonlinear Schrödinger equations
• Semiclassical states of nonlinear Schrödinger equations
• Multi-peak bound states for nonlinear Schrödinger equations
• Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations
• On a singularly perturbed elliptic equation
• Existence and semi-classical limit of the least energy solution to a nonlinear Schrödinger equation with electromagnetic fields
• Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields
• Semiclassical stationary states of nonlinear Schrödinger equations with an external magnetic field.
• A semilinear Schrödinger equation in the presence of a magnetic field
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
• On the Schrödinger equation involving a critical Sobolev exponent and magnetic field
• ON THE LOCATION OF SPIKES FOR THE SCHRÖDINGER EQUATION WITH ELECTROMAGNETIC FIELD
• Semiclassical states for NLS equations with magnetic potentials having polynomial growths
• Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields
• Variational perturbative methods and bifurcation of bound states from the essential spectrum
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Strong Carleman operators are of Hilbert-Schmidt type
• Multiplicity results for some nonlinear Schrödinger equations with potentials
• Existence of positive solutions for a class of indefinite elliptic problems in \(\mathbb{R}^N\)