Solutions, concentrating on spheres, to symmetric singularly perturbed problems

Antonio Ambrosetti; Andrea Malchiodi; Wei-Ming Ni

doi:10.1016/S1631-073X(02)02414-7

Solutions, concentrating on spheres, to symmetric singularly perturbed problems
[Solutions concentreés sur spheres des problèmes de perturbation singulière]

Antonio Ambrosetti ¹ ; Andrea Malchiodi ² ; Wei-Ming Ni ³

¹ SISSA, via Beirut 2-4, 34014 Trieste, Italy
² School of Math., Institute for Advanced Study, Princeton, NJ 08540, USA
³ School of Math., Univ. of Minnesota, Minneapolis, MN 55455, USA

Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 145-150

Abstract (VO)
Résumé

We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.

Nous étudions des problèmes de perturbations singulières (NLS), (N). On montre l'existence de solutions positives qui se concentrent sur une sphère.

Accepté le : 2002-04-08
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02414-7

Affiliations des auteurs :

Antonio Ambrosetti ¹ ; Andrea Malchiodi ² ; Wei-Ming Ni ³

¹ SISSA, via Beirut 2-4, 34014 Trieste, Italy
² School of Math., Institute for Advanced Study, Princeton, NJ 08540, USA
³ School of Math., Univ. of Minnesota, Minneapolis, MN 55455, USA

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     author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni},
     title = {Solutions, concentrating on spheres, to symmetric singularly perturbed problems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {145--150},
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     publisher = {Elsevier},
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     number = {2},
     doi = {10.1016/S1631-073X(02)02414-7},
     language = {en},
}

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Antonio Ambrosetti; Andrea Malchiodi; Wei-Ming Ni. Solutions, concentrating on spheres, to symmetric singularly perturbed problems. Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 145-150. doi: 10.1016/S1631-073X(02)02414-7

Bibliographie
Cité par

[1] A. Ambrosetti; M. Badiale Proc. Roy. Soc. Edinburg Sect. A, 128 (1998), pp. 1131-1161

[2] A. Ambrosetti; M. Badiale; S. Cingolani Arch. Rational Mech. Anal., 140 (1997), pp. 285-300

[3] A. Ambrosetti, A. Malchiodi, W.-M. Ni, Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, to appear

[4] A. Ambrosetti; A. Malchiodi; S. Secchi Arch. Rational Mech. Anal., 159 (2001), pp. 253-271

[5] M. Badiale, T. D'Aprile, Concentration around a ssphere for a singularly perturbed Schrödinger equation, Preprint, Scuola Normale Superiore

[6] A. Malchiodi, M. Montenegro, Boundary concentration phenomena for a singularly perturbed elliptic problem, Comm. Pure Appl. Math., to appear

[7] W.-M. Ni Notices Amer. Math. Soc., 45 (1998) no. 1, pp. 9-18

[8] W.-M. Ni; I. Takagi Duke Math. J., 70 (1993), pp. 247-281

[9] W.-M. Ni; J. Wei Comm. Pure Appl. Math., 48 (1995), pp. 731-768

[10] X. Wang Comm. Math. Phys., 153 (1993), pp. 229-243

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