Geodesic
Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 2, pp. 81-86 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2004_9_15_2_a1,
     author = {Ambrosetti, Antonio and Felli, Veronica and Malchiodi, Andrea},
     title = {Ground {States} of {Nonlinear} {Schr\"odinger} {Equations} with potentials vanishing at infinity},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {81--86},
     year = {2004},
     volume = {Ser. 9, 15},
     number = {2},
     zbl = {1225.35213},
     mrnumber = {MR2148536},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_2_a1/}
}
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Ambrosetti, Antonio; Felli, Veronica; Malchiodi, Andrea. Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 2, pp. 81-86. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_2_a1/