Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent

DOI10.1007/s11784-011-0053-0zbMath1273.35247arXiv1009.3386OpenAlexW1976736119MaRDI QIDQ644463

Susanna Terracini, Laura Abatangelo

Publication date: 4 November 2011

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.3386

zbMATH Keywords

nonlinear Schrödinger equationsHardy's inequalitysingular electromagnetic potentials

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20) Singular elliptic equations (35J75) Symmetries, invariants, etc. in context of PDEs (35B06) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (9)

Segregated vector solutions for nonlinear Schrödinger systems with electromagnetic potentials ⋮ On Caffarelli-Kohn-Nirenberg inequalities for block-radial functions ⋮ Unnamed Item ⋮ Multiple solutions to nonlinear Schrödinger equations with singular electromagnetic potential ⋮ The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field ⋮ Ground state solutions for Schrödinger problems with magnetic fields and Hardy-Sobolev critical exponents ⋮ Multiple solutions for a semilinear elliptic equation with critical growth and magnetic field ⋮ Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations ⋮ Multiple solutions to a nonlinear Schrödinger equation with Aharonov-Bohm magnetic potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
• On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
• On multi-bump semi-classical bound states of nonlinear Schrödinger equations with electromagnetic fields
• On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity
• Multiple solutions to a nonlinear Schrödinger equation with Aharonov-Bohm magnetic potential
• New estimates for elliptic equations and Hodge type systems
• On nontrivial solutions of a nonlinear Schrödinger equation with magnetic field
• 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
• A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• On the Schrödinger equation involving a critical Sobolev exponent and magnetic field
• A Note on the Complete Rotational Invariance of Biradial Solutions to Semilinear Elliptic Equations
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Intertwining semiclassical bound states to a nonlinear magnetic Schrödinger equation
• Semiclassical states for NLS equations with magnetic potentials having polynomial growths
• Periodic and Bloch Solutions to a Magnetic Nonlinear Schrödinger Equation
• A unique continuation theorem for the Schrödinger equation with singular magnetic field

This page was built for publication: Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent