Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 272, Issue 12, Pages 5255-5281Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2017.02.026
Keywords
Planar Schrodinger-Newton system; Positive ground state solution; Asymptotics; Nondegeneracy
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Funding
- GNAMPA project Studio variazionale di fenomeni fisici non lineari
- Projet de Recherche (Fonds de la Recherche Scientifique - FNRS) [T.1110.14]
- Mandat d'Impulsion Scientifique Fonds de la Recherche Scientifique - FNRS [F.4508.14]
- Actions de Recherche Concertee (ARC) [AUWB-2012-12/17-ULB1-IAPAS]
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We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation -Delta u + au = 1/2 pi [ln 1/vertical bar x vertical bar * vertical bar u vertical bar(2)] u in R-2 and we establish its nondegeneracy. For the corresponding three-dimensional problem, the nondegeneracy property of the positive ground state to the Choquard equation was proved by E. Lenzmann (2009) [13]. (C) 2017 Elsevier Inc. All rights reserved.
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