Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

A. Ambrosettia1 and D. Ruiza2

a1 SISSA, 2–4 via Beirut, Trieste 34014, Italy (

a2 SISSA, 2–4 via Beirut, 34014 Trieste, Italy and Departamento de Análisis Matemático Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain* (


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.

(Received June 01 2005)

(Accepted October 05 2005)


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