Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres
(2012) Journal of Differential Equations — Vol. 252, n° 2, p. 941-968 (2012)
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- Authors
- 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.
- Affiliations
Université Libre de Bruxelles Département de Mathématique
Citations
Van Schaftingen, J., Di Cosmo, J., & Van Schaftingen, J. (2012). Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres. Journal of Differential Equations, 252(2), 941-968. https://doi.org/10.1016/j.jde.2011.10.004 (Original work published 2012)