Nonlinear Schrödinger equations with strongly singular potentials

DOI10.1017/S0308210509001401zbMath1197.35263arXiv0903.3301MaRDI QIDQ3580647

Claudio Bonanno, Jacopo Bellazzini

Publication date: 13 August 2010

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3301

zbMATH Keywords

nonlinear Schrödinger equationsstanding waveshydrogen atom equationminimization arguments

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Variational methods applied to PDEs (35A15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Atomic physics (81V45) Applications of operator theory to differential and integral equations (47N20)

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Self-bound vortex states in nonlinear Schrödinger equations with LHY correction ⋮ Hylomorphic solitons ⋮ The Wigner(–Poisson)–Fokker–Planck equation with singular potential ⋮ A minimization method and applications to the study of solitons ⋮ Stable standing waves for a class of nonlinear Schrödinger-Poisson equations ⋮ Scaling properties of functionals and existence of constrained minimizers ⋮ Soliton dynamics for the generalized Choquard equation ⋮ Orbital stability for the Schrödinger operator involving inverse square potential ⋮ Spinning Q-balls for the Klein-Gordon-Maxwell equations ⋮ Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations

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