# A priori estimates, uniqueness and non-degeneracy of positive solutions of the Choquard equation

@inproceedings{Li2022APE, title={A priori estimates, uniqueness and non-degeneracy of positive solutions of the Choquard equation}, author={Zexing Li}, year={2022} }

We consider the positive solutions for the nonlocal Choquard equation −∆u+ u− (| · | ∗ |u|)|u|u = 0 in R. Compared with ground states, positive solutions form a larger class of solutions and lack variational information. Within the range of parameters of Ma-Zhao’s result [25] on symmetry, we prove a priori estimates for positive solutions, generalizing the classical method of De Figueiredo-Lions-Nussbaum [10] to the unbounded domain and the nonlocal nonlinearity in our model. As an application…

## One Citation

### Threshold solutions for the focusing generalized Hartree equations

- Mathematics
- 2022

. We study the global behavior of solutions to the focusing generalized Hartree equation with H 1 data at mass-energy threshold in the inter-range case. In the earlier works of Arora-Roudenko [2],…

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