The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstate

Abstract : We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation −∆u + au = 1 2π ln 1 |x| * |u| 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 (Analysis & PDE, 2009).
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Submitted on : Monday, December 12, 2016 - 9:00:31 AM
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Denis Bonheure, Silvia Cingolani, Jean Van Schaftingen. The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstate. 2016. ⟨hal-01414010⟩

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