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Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials

Published online by Cambridge University Press:  12 July 2007

A. Ambrosetti
Affiliation:
SISSA, 2–4 via Beirut, Trieste 34014, Italy (ambr@sissa.it)
D. Ruiz
Affiliation:
SISSA, 2–4 via Beirut, 34014 Trieste, Italy and Departamento de Análisis Matemático Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain* (daruiz@ugr.es)

Abstract

We prove the existence of radial solutions of concentrating on a sphere for potentials which might be zero and might decay to zero at infinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov–Schmidt reduction.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2006

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