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Nonlinear Schrödinger equations with strongly singular potentials

Published online by Cambridge University Press:  04 August 2010

Jacopo Bellazzini  and
Claudio Bonanno
Jacopo Bellazzini
Affiliation:
Dipartimento di Matematica Applicata ‘U. Dini’, Università di Pisa, via Buonarroti 1/c, 56127 Pisa, Italy ([email protected]; [email protected])
Claudio Bonanno
Affiliation:
Dipartimento di Matematica Applicata ‘U. Dini’, Università di Pisa, via Buonarroti 1/c, 56127 Pisa, Italy ([email protected]; [email protected])
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Abstract

We look for standing waves for nonlinear Schrödinger equations

with cylindrically symmetric potentials g vanishing at infinity and non-increasing, and a C1 nonlinear term satisfying weak assumptions. In particular, we show the existence of standing waves with non-vanishing angular momentum with prescribed L2 norm. The solutions are obtained via a minimization argument, and the proof is given for an abstract functional which presents a lack of compactness. As a specific case, we prove the existence of standing waves with non-vanishing angular momentum for the nonlinear hydrogen atom equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 4 , August 2010 , pp. 707 - 721
Copyright
Copyright © Royal Society of Edinburgh 2010

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