Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres

Details Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres

2010-09-14

arxiv.org/abs/1009.2600v1

J. Differential Equations 252 (2012), 941-968

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.jde.2011.10.004

We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows us to consider broader classes of potentials than those treated in previous works. For example, the potentials might be singular at the origin or vanish superquadratically at infinity.

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