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A guide to the Choquard equation
V Moroz, J Van Schaftingen - Journal of Fixed Point Theory and …, 2017 - Springer
We survey old and recent results dealing with the existence and properties of solutions to
the Choquard type equations-Δ u+ V (x) u=\left (| x|^-(N-α)*| u|^ p\right)| u|^ p-2 u\quad …
the Choquard type equations-Δ u+ V (x) u=\left (| x|^-(N-α)*| u|^ p\right)| u|^ p-2 u\quad …
On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation
F Gao, M Yang - arxiv preprint arxiv:1604.00826, 2016 - arxiv.org
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear
Choquard equation $$-\Delta u=\left (\int_ {\Omega}\frac {| u|^{2_ {\mu}^{\ast}}}{| xy|^{\mu}} …
Choquard equation $$-\Delta u=\left (\int_ {\Omega}\frac {| u|^{2_ {\mu}^{\ast}}}{| xy|^{\mu}} …
Existence of groundstates for a class of nonlinear Choquard equations
V Moroz, J Van Schaftingen - Transactions of the American Mathematical …, 2015 - ams.org
We prove the existence of a nontrivial solution $ u\in H^ 1 (\mathbb {R}^ N) $ to the
nonlinear Choquard equation\[-\Delta u+ u=\bigl (I_\alpha\ast F (u)\bigr) F'(u)\quad\text …
nonlinear Choquard equation\[-\Delta u+ u=\bigl (I_\alpha\ast F (u)\bigr) F'(u)\quad\text …
Normalized solutions for lower critical Choquard equations with critical Sobolev perturbation
S Yao, H Chen, VD Rădulescu, J Sun - SIAM Journal on Mathematical …, 2022 - SIAM
We study normalized solutions for the following Choquard equations with lower critical
exponent and a local perturbation -Δu+λu=γ(I_α∗|u|^αN+1)|u|^αN-1u+μ|u|^q …
exponent and a local perturbation -Δu+λu=γ(I_α∗|u|^αN+1)|u|^αN-1u+μ|u|^q …
On fractional Choquard equations
On fractional Choquard equations | Mathematical Models and Methods in Applied Sciences
World Scientific Search This Journal Anywhere Quick Search in Journals Enter words …
World Scientific Search This Journal Anywhere Quick Search in Journals Enter words …
Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
V Moroz, J Van Schaftingen - Communications in Contemporary …, 2015 - World Scientific
We consider nonlinear Choquard equation where N≥ 3, V∈ L∞(ℝN) is an external
potential and Iα (x) is the Riesz potential of order α∈(0, N). The power in the nonlocal part of …
potential and Iα (x) is the Riesz potential of order α∈(0, N). The power in the nonlocal part of …
[HTML][HTML] Singularly perturbed critical Choquard equations
In this paper we study the semiclassical limit for the singularly perturbed Choquard
equation− ε 2 Δ u+ V (x) u= ε μ− 3 (∫ R 3 Q (y) G (u (y))| x− y| μ dy) Q (x) g (u) in R 3, where …
equation− ε 2 Δ u+ V (x) u= ε μ− 3 (∫ R 3 Q (y) G (u (y))| x− y| μ dy) Q (x) g (u) in R 3, where …
Semi-classical states for the Choquard equation
V Moroz, J Van Schaftingen - Calculus of Variations and Partial Differential …, 2015 - Springer
We study the nonlocal equation-ε^ 2 Δ u_ ε+ V u_ ε= ε^-α\bigl (I_ α*| u_ ε|^ p\bigr)| u_ ε|^ p-2
u_ ε\quad in R^ N,-ε 2 Δ u ε+ V u ε= ε-α (I α∗| u ε| p)| u ε| p-2 u ε in RN, where N ≥ 1 N≥ 1, α …
u_ ε\quad in R^ N,-ε 2 Δ u ε+ V u ε= ε-α (I α∗| u ε| p)| u ε| p-2 u ε in RN, where N ≥ 1 N≥ 1, α …
Nonlinear fractional schrödinger equations in
V Ambrosio - RN (Birkhäuser, 2021), 2021 - Springer
The aim of this book is to collect a set of results concerning nonlinear Schrödinger equations
in the whole space driven by fractional operators. The material presented here was mainly …
in the whole space driven by fractional operators. The material presented here was mainly …
[HTML][HTML] Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2
We study the following singularly perturbed nonlocal Schrödinger equation− ε 2 Δ u+ V (x)
u= ε μ− 2 [1| x| μ⁎ F (u)] f (u) in R 2, where V (x) is a continuous real function on R 2, F (s) is …
u= ε μ− 2 [1| x| μ⁎ F (u)] f (u) in R 2, where V (x) is a continuous real function on R 2, F (s) is …