# Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity

Antonio Ambrosetti; Veronica Felli; Andrea Malchiodi

- Volume: 15, Issue: 2, page 81-86
- ISSN: 1120-6330

## Access Full Article

top## Abstract

top## How to cite

topAmbrosetti, Antonio, Felli, Veronica, and Malchiodi, Andrea. "Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.2 (2004): 81-86. <http://eudml.org/doc/252395>.

@article{Ambrosetti2004,

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.},

author = {Ambrosetti, Antonio, Felli, Veronica, Malchiodi, Andrea},

journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},

keywords = {Nonlinear Schrödinger equations; Weighted Sobolev spaces; Critical point theory; nonlinear Schrödinger equations; weighted Sobolev spaces; critical point theory},

language = {eng},

month = {6},

number = {2},

pages = {81-86},

publisher = {Accademia Nazionale dei Lincei},

title = {Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity},

url = {http://eudml.org/doc/252395},

volume = {15},

year = {2004},

}

TY - JOUR

AU - Ambrosetti, Antonio

AU - Felli, Veronica

AU - Malchiodi, Andrea

TI - Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity

JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

DA - 2004/6//

PB - Accademia Nazionale dei Lincei

VL - 15

IS - 2

SP - 81

EP - 86

AB - 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.

LA - eng

KW - Nonlinear Schrödinger equations; Weighted Sobolev spaces; Critical point theory; nonlinear Schrödinger equations; weighted Sobolev spaces; critical point theory

UR - http://eudml.org/doc/252395

ER -

## References

top- AMBROSETTI, A. - BADIALE, M., Homoclinics: Poincaré-Melnikov type results via a variational approach. Ann. Inst. H. Poincaré Analyse Non Linéaire, 15, 1998, 233-252. Zbl1004.37043MR1614571DOI10.1016/S0294-1449(97)89300-6
- AMBROSETTI, A. - FELLI, V. - MALCHIODI, A., Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. Preprint S.I.S.S.A., n. 16/2004/M, Febr. 2004; to appear on Journal Europ. Math. Soc. Zbl1064.35175MR2148536
- AMBROSETTI, A. - MALCHIODI, A. - SECCHI, S., Multiplicity results for some nonlinear singularly perturbed elliptic problems on ${\mathbb{R}}^{n}$. Arch. Rat. Mech. Anal., 159, 2001, 253-271. Zbl1040.35107MR1857674DOI10.1007/s002050100152
- LI, Y.Y., On a singularly perturbed elliptic equation. Adv. Diff. Eqns., 2, 1997, 955-980. Zbl1023.35500MR1606351
- NOUSSAIR, E.S. - SWANSON, C.A., Decaying solutions of semilinear elliptic equations in ${\mathbb{R}}^{N}$. SIAM J. Math. Anal., 20, 6, 1989, 1336-1343. Zbl0696.35051MR1019304DOI10.1137/0520088
- OPIC, B. - KUFNER, A., Hardy-type inequalities. Pitman Res. Notes in Math. Series219, Longman Scientific & Technical, Harlow1990. Zbl0698.26007MR1069756
- SCHNEIDER, M., Entire solutions of semilinear elliptic problems with indefinite nonlinearities. PhD Thesis, Universität Mainz, 2001. Zbl1134.35347

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.