• Corpus ID: 245650840

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… 
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References

SHOWING 1-10 OF 48 REFERENCES

Uniqueness of non-linear ground states for fractional Laplacians in R

Fractionalpowers of the Laplacian arise in a numerous variety of equations in mathematical physics and related fields; see, e.g., [1], [9], [14], [17], [20], [24], [28], [34] and the references

Classification of Positive Solitary Solutions of the Nonlinear Choquard Equation

AbstractIn this paper, we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary Choquard equation $$\Delta

Uniqueness of Radial Solutions for the Fractional Laplacian

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (−Δ)s with s ∊ (0,1) for any space dimensions N ≥ 1. By extending a

Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

The equation dealt with in this paper is in three dimensions. It comes from minimizing the functional which, in turn, comes from an approximation to the Hartree-Fock theory of a plasma. It describes

Global Behavior of Solutions to the Focusing Generalized Hartree Equation

We study the global behavior of solutions to the nonlinear generalized Hartree equation, where the nonlinearity is of the non-local type and is expressed as a convolution, $$ i u_t + \Delta u +

Uniqueness of ground states for pseudorelativistic Hartree equations

We prove uniqueness of ground states Q ∈ H 1/2 (R 3 ) for the pseudo-relativistic Hartree equation, p −� + m 2 Q − ` |x| 1 ∗ |Q| 2 ´ Q = −µQ, in the regime of Q with sufficiently smallL 2 -mass. This

Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0

On considere le probleme de l'unicite pour les solutions positives du probleme de Dirichlet non lineaire Δu+f(u,|x|)=0 dans Ω, u/ ∂Ω =0, Ω est une boule ou un anneau de R n et f≥0 est superlineaire

Threshold solutions for the focusing generalized Hartree equations

. 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],