Existence of solutions for semilinear elliptic problems in exterior of ball

Jacopo Bellazzini

doi:10.1016/j.crma.2010.03.017

Partial Differential Equations

Existence of solutions for semilinear elliptic problems in exterior of ball
[Existence des solutions pour des problèmes elliptiques non linéaires à extérieur de la boule]

Présenté par : Haïm Brezis

Jacopo Bellazzini ¹

¹ Dipartimento di Matematica Applicata Università di Pisa, Via Buonarroti 1/C, 56127 Pisa, Italy

Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 545-548.

Résumé
Abstract

Dans cette Note, nous demontrons l'existence d'une solution pour des équation elliptiques non linéaires in $Ω = B {(0, R)}^{c}$ , $N ⩾ 3$

- Δ u = G^{'} (u),

pour a general nonlinéarité G.

We prove the existence of solutions for the semilinear elliptic problem in $Ω = B {(0, R)}^{c}$ , $N ⩾ 3$ .

- Δ u = G^{'} (u),

under suitable general assumptions on the nonlinear term G.

Reçu le : 2010-02-12
Accepté le : 2010-03-18
Publié le : 2010-04-24

DOI : 10.1016/j.crma.2010.03.017

Affiliations des auteurs :

Jacopo Bellazzini ¹

¹ Dipartimento di Matematica Applicata Università di Pisa, Via Buonarroti 1/C, 56127 Pisa, Italy

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     author = {Jacopo Bellazzini},
     title = {Existence of solutions for semilinear elliptic problems in exterior of ball},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {545--548},
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     volume = {348},
     number = {9-10},
     year = {2010},
     doi = {10.1016/j.crma.2010.03.017},
     language = {en},
}

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Jacopo Bellazzini. Existence of solutions for semilinear elliptic problems in exterior of ball. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 545-548. doi : 10.1016/j.crma.2010.03.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.017/

Bibliographie
Cité par

[1] A. Ambrosetti; P.H. Rabinowitz Dual variational methods in critical point theory and applications, J. Funct. Anal., Volume 14 (1973), pp. 349-381

[2] A. Azzollini; A. Pomponio On the Schrödinger equation in $R^{N}$ under the effect of a general nonlinear term, Indiana Univ. Math. J., Volume 58 (2009) no. 3, pp. 1361-1378

[3] H. Berestycki; P.L. Lions Nonlinear scalar field equations. I. Existence of a ground state, Arch. Ration. Mech. Anal., Volume 82 (1982), pp. 313-345

[4] L. Jeanjean; K. Tanaka A positive solution for a nonlinear Schrödinger equation in $R^{N}$ , Indiana Univ. Math. J., Volume 54 (2005) no. 2, pp. 443-464

[5] M. Lucia A mountain pass theorem without Palais–Smale condition, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 341 (2005) no. 5, pp. 287-291

[6] W. Strauss Existence of solitary waves in higher dimensions, Comm. Math. Phys., Volume 55 (1977) no. 2, pp. 149-162

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