We deal with a class on nonlinear Schrödinger equations with potentials vanishing at infinity. Working in weighted Sobolev spaces, the existence of a ground state is proved. Furthermore, the behaviour of such a solution, as the Planck constant tends to zero (semiclassical limit), is studied proving that it concentrates at a point.
Ambrosetti, A., Felli, V., Malchiodi, A. (2005). Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 7(1), 117-144 [10.4171/JEMS/24].
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
FELLI, VERONICA;
2005
Abstract
We deal with a class on nonlinear Schrödinger equations with potentials vanishing at infinity. Working in weighted Sobolev spaces, the existence of a ground state is proved. Furthermore, the behaviour of such a solution, as the Planck constant tends to zero (semiclassical limit), is studied proving that it concentrates at a point.
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