Nonlinear Schrödinger equations with strongly singular potentials

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dc.creatorBellazzini, Jacopo
dc.creatorBonanno, Claudio
dc.date2009-03-19
dc.date.accessioned2026-07-07T12:54:14Z
dc.date.available2026-07-07T12:54:14Z
dc.descriptionIn this paper we look for standing waves for nonlinear Schrödinger equations $$ i\frac{\partial ψ}{\partial t}+Δψ- g(|y|) ψ-W^{\prime}(| ψ|)\fracψ{| ψ|}=0 $$ with cylindrically symmetric potentials $g$ vanishing at infinity and non-increasing, and a $C^1$ nonlinear term satisfying weak assumptions. In particular we show the existence of standing waves with non-vanishing angular momentum with prescribed $L^2$ norm. The solutions are obtained via a minimization argument, and the proof is given for an abstract functional which presents lack of compactness. As a particular case we prove the existence of standing waves with non-vanishing angular momentum for the nonlinear hydrogen atom equation.
dc.identifierhttps://arxiv.org/abs/0903.3301
dc.identifierhttp://arxiv.org/abs/0903.3301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223860
dc.subjectMathematical Physics
dc.titleNonlinear Schrödinger equations with strongly singular potentials
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