Nonlinear Schr\"odinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres
Analysis of PDEs
2011-11-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1009.2600,
title = {Nonlinear Schr\"odinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres},
author = {Denis Bonheure and Jonathan Di Cosmo and Jean Van Schaftingen},
journal= {arXiv preprint arXiv:1009.2600},
year = {2011}
}