Comptes Rendus
Solutions, concentrating on spheres, to symmetric singularly perturbed problems
[Solutions concentreés sur spheres des problèmes de perturbation singulière]
Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 145-150.

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

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

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02414-7
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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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02414-7/

[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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