Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently close to 2. By investigating the limit profile...

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Bibliographic Details
Main Authors: Luo Huxiao, Zhang Dingliang, Xu Yating
Format: Article
Language:English
Published: De Gruyter 2024-11-01
Series:Advances in Nonlinear Analysis
Subjects:
limit profile
choquard equation
uniqueness and nondegeneracy
35a02
35b20
35j61
Online Access:https://doi.org/10.1515/anona-2024-0048
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