Existence and concentration for nonlinear Schrodinger equations with fast decaying potentials

Moroz, Vitaly;Van Schaftingen, Jean
(2009) Comptes rendus - Mathématique — Vol. 347, n° 15-16, p. 921-926 (2009)

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Abstract
The existence of positive solutions to -epsilon(2) Delta u + Vu = u(p) in R-N, is proved for small epsilon, where N >= 3, V is a nonnegative continuous potential which has a positive local minimum, and N/N-2 < p < N+2/N-2 . No restriction is imposed on the rate of decay of V; this includes in particular the case where V is compactly supported. To cite this article: V. Moroz, J. Van Schaftingen, C. R. Acad. Sci. Paris, Ser. I 347 (2009). (c) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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Moroz, V., & Van Schaftingen, J. (2009). Existence and concentration for nonlinear Schrodinger equations with fast decaying potentials. Comptes rendus - Mathématique, 347(15-16), 921-926. https://doi.org/10.1016/j.crma.2009.05.009 (Original work published 2009)