In this preliminary note we outline the results of the forthcoming paper [2] dealing 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. (2004). Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 15(2), 81-86.
Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity
FELLI, VERONICA;
2004
Abstract
In this preliminary note we outline the results of the forthcoming paper [2] dealing 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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