Nonlinear Schrödinger equations with inverse-square potentials in two dimensional space

DOI10.3934/proc.2015.1019zbMath1336.35324OpenAlexW2331437063MaRDI QIDQ260948

Toshiyuki Suzuki

Publication date: 22 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/proc.2015.1019

zbMATH Keywords

energy methodsnonlinear Schrödinger equationsinverse-square potentials

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (2)

On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction ⋮ Existence and orbital stability of standing waves to a nonlinear Schrödinger equation with inverse square potential on the half-line

Cites Work

• Isolated singularity for semilinear elliptic equations
• Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
• Energy methods for abstract nonlinear Schrödinger equations
• Energy methods for Hartree type equations with inverse-square potentials
• Solvability of Nonlinear Schrödinger Equations with Some Critical Singular Potential via Generalized Hardy-Rellich Inequalities
• Cauchy problem for nonlinear Schrödinger equations with inverse-square potentials
• Critical case of nonlinear Schrödinger equations with inverse-square potentials on bounded domains
• A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations

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