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Paper detail

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

We study positive bound states for the semiclassical stationary nonlinear Schrödinger 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.

preprint2010arXivOpen access
Denis BonheureJonathan Di CosmoJean Van Schaftingen
math.AP
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Denis BonheureJonathan Di CosmoJean Van Schaftingen

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