Normalized ground states for the Schrödinger equation with Hartree type and square-root nonlinearities

DOI10.1007/S00009-023-02538-4MaRDI QIDQ6181563

Anmin Mao, Shuyao Lu

Publication date: 22 January 2024

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationHartree typesquare-root nonlinearitysquare-root nonlinearity Dinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Nonlinear elliptic equations (35J60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for second-order elliptic equations (35J20)

Cites Work

• Nodal solutions for the Choquard equation
• Mass minimizers and concentration for nonlinear Choquard equations in \({\mathbb R}^N\)
• Nonlinear Schrödinger equations and sharp interpolation estimates
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in \(\mathbb{R}^2\) with square root and saturable nonlinearities in nonlinear optics
• Nonlinear Choquard equations with Hardy-Littlewood-Sobolev critical exponents
• Normalized solutions to the planar Schrödinger-Poisson systems with square-root nonlinearity
• Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
• Multi-bump solutions for Choquard equation with deepening potential well
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• On nonlocal Choquard system with Hardy-Littlewood-Sobolev critical exponents

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