The logarithmic Choquard equation: Sharp asymptotics and nondegeneracy of the groundstate
(2017) Journal of Functional Analysis — Vol. 272, n° 12, p. 5255-5281 (2017)
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- Abstract
- We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation −Δu+au=1/(2π) [ln1|x|∗|u|²] u in ℝ² 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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Bonheure, D., Cingolani, S., & Van Schaftingen, J. (2017). The logarithmic Choquard equation: Sharp asymptotics and nondegeneracy of the groundstate. Journal of Functional Analysis, 272(12), 5255-5281. https://doi.org/10.1016/j.jfa.2017.02.026 (Original work published 2017)