Standing waves for nonlinear Schrödinger equations with singular potentials

DOI10.1016/j.anihpc.2008.03.009zbMath1177.35215OpenAlexW2068470326MaRDI QIDQ1030145

Zhi-Qiang Wang, Jaeyoung Byeon

Publication date: 1 July 2009

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/78875

zbMATH Keywords

nonlinear Schrödinger equationsdecaying and unbounded potentialssingularities of potentials

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (14)

Infinitely many solutions of degenerate quasilinear Schrödinger equation with general potentials ⋮ New singular standing wave solutions of the nonlinear Schrödinger equation ⋮ On the existence and multiplicity of solutions for a class of singular elliptic problems ⋮ Sobolev type embedding and quasilinear elliptic equations with radial potentials ⋮ Localization of normalized solutions for saturable nonlinear Schrödinger equations ⋮ Multiple positive standing wave solutions for Schrödinger equations with oscillating state-dependent potentials ⋮ Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials ⋮ Ground states of degenerate quasilinear Schrödinger equation with vanishing potentials ⋮ Bound states for logarithmic Schrödinger equations with potentials unbounded below ⋮ The existence of least energy and high energy solutions to the Kirchhoff type problem in high dimensions ⋮ Semiclassical states for nonlinear Dirac equations with singular potentials ⋮ Semi-classical states for logarithmic Schrödinger equations ⋮ Limiting profile of solutions for Schrödinger equations with shrinking self-focusing core ⋮ Positive solutions for a class of elliptic systems with singular potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Nonlinear Schrödinger equations with vanishing and decaying potentials.
• On a class of nonlinear Schrödinger equations
• Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I
• Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
• Standing waves with a critical frequency for nonlinear Schrödinger equations
• On the existence of multipeak solutions for nonlinear field equations on \(\mathbb R^N\).
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Semi-classical states of nonlinear Schrödinger equations: a variational reduction method
• Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity
• Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials
• Standing waves for nonlinear Schrödinger equations with a general nonlinearity
• Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Existence of Multi-bump Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
• On interacting bumps of semi-classical states of nonlinear Schrödinger equations.

This page was built for publication: Standing waves for nonlinear Schrödinger equations with singular potentials