Comptes Rendus
Partial Differential Equations
Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials
Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 921-926.

The existence of positive solutions to

ε2Δu+Vu=upin RN,
is proved for small ε, where N3, V is a nonnegative continuous potential which has a positive local minimum, and NN2<p<N+2N2. No restriction is imposed on the rate of decay of V; this includes in particular the case where V is compactly supported.

Nous prouvons l'existence de solutions positives non triviales de

ε2Δu+Vu=updans RN,
pour ε petit, où N3, V est potentiel continu positif qui a un minimum local strictement positif et NN2<p<N+2N2. Nous n'imposons aucune restriction sur le taux de décroisance de V. En particulier, nous couvrons le cas où le support de V est compact.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.05.009

Vitaly Moroz 1; Jean Van Schaftingen 2

1 Swansea University, Department of Mathematics, Singleton Park, Swansea SA2 8PP, Wales, United Kingdom
2 Université Catholique de Louvain, département de mathématique, chemin du cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
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     title = {Existence and concentration for nonlinear {Schr\"odinger} equations with fast decaying potentials},
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Vitaly Moroz; Jean Van Schaftingen. Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 921-926. doi : 10.1016/j.crma.2009.05.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.05.009/

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