Results 91 to 100 of about 1,494,768 (123)
Some of the next articles are maybe not open access.
Normalized solution for fractional Choquard equation with potential and general nonlinearity
Complex Variables and Elliptic Equations, 2023In this paper, we consider the following fractional Choquard equation: \[ \begin{cases} (-\Delta)^s u+V(x) u+\lambda u=(I_\alpha\ast F(u))f(u)\quad \mathrm{in}\ \mathbb{R}^{N},\\ \displaystyle\int_{\mathbb{R}^{N}} u^{2}\,\mathrm{d} x=\rho^{2},\ \rho>0 ...
Zhentao Jin +3 more
semanticscholar +1 more source
Liouville‐type theorems for a nonlinear fractional Choquard equation
Mathematische Nachrichten, 2023In this paper, we are concerned with the fractional Choquard equation on the whole space RN$\mathbb {R}^N$ (−Δ)su=1|x|N−2s∗upup−1$$\begin{equation*} \hspace*{7pc}(-\Delta )^s u={\left(\frac{1}{|x|^{N-2s}}*u^p\right)}u^{p-1} \end{equation*}$$with 02s$N>2s$
A. Duong +3 more
semanticscholar +1 more source
Normalized solutions for fractional Choquard equation with critical growth on bounded domain
Nonlinear Differential Equations and Applications NoDEAIn this work, we establish the multiplicity of positive solutions for the following critical fractional Choquard equation with a perturbation on the star-shaped bounded domain (-Δ)su=λu+α|u|p-2u+∫Ω|u(y)|2μ,s∗|x-y|μdy|u|2μ,s∗-2uinΩ,u>0inΩ,u=0inRN\Ω,∫Ω|u ...
Divya Goel, Asmita Rai
semanticscholar +1 more source
Mathematical methods in the applied sciences
In this paper, we consider the following fractional Choquard equation: (−Δ)su+V(x)u+λu=(Iα∗|u|2α,s∗)|u|2α,s∗−2u+μ|u|q−2u,x∈ℝN$$ {\left(-\Delta \right)}^su+V(x)u+\lambda u=\left({I}_{\alpha}\ast {\left|u\right ...
Peng Ji, Fangqi Chen
semanticscholar +1 more source
In this paper, we consider the following fractional Choquard equation: (−Δ)su+V(x)u+λu=(Iα∗|u|2α,s∗)|u|2α,s∗−2u+μ|u|q−2u,x∈ℝN$$ {\left(-\Delta \right)}^su+V(x)u+\lambda u=\left({I}_{\alpha}\ast {\left|u\right ...
Peng Ji, Fangqi Chen
semanticscholar +1 more source
, 2020
In this paper, we study the nonlinear Choquard equation e2s(−Δ)su+V(x)u=Iα*|u|2α,s*|u|2α,s*−2u,u∈Ds,2(RN), where s ∈ (0, 1), N ≥ 3, ɛ is the positive parameter, and 2α,s*=N+αN−2s is the critical exponent with respect to the Hardy–Littlewood–Sobolev ...
Lun Guo, Qi Li
semanticscholar +1 more source
In this paper, we study the nonlinear Choquard equation e2s(−Δ)su+V(x)u=Iα*|u|2α,s*|u|2α,s*−2u,u∈Ds,2(RN), where s ∈ (0, 1), N ≥ 3, ɛ is the positive parameter, and 2α,s*=N+αN−2s is the critical exponent with respect to the Hardy–Littlewood–Sobolev ...
Lun Guo, Qi Li
semanticscholar +1 more source
Normalized Ground States for the Critical Fractional Choquard Equation with a Local Perturbation
Journal of Geometric Analysis, 2022Xiao-Ming He +2 more
semanticscholar +1 more source
Potential well theory for the focusing fractional Choquard equation
, 2020This note studies the non-linear fractional Schrodinger equation iu−(−Δ)su+(Iα*|u|p)|u|p−2u=0. In the mass super-critical and energy sub-critical regimes, the local solutions exist globally and scatter in the energy space or blow-up in finite time if the
T. Saanouni
semanticscholar +1 more source
Strong instability of standing waves for the fractional Choquard equation
Journal of Mathematics and Physics, 2018Using variational methods and the potential well theory, strong instability of standing waves for a class of fractional Schrodinger-Choquard equations is established in the mass super-critical and energy sub-critical case.Using variational methods and ...
T. Saanouni
semanticscholar +1 more source
The Benci–Cerami problem for the fractional Choquard equation with critical exponent
Manuscripta mathematica, 2022Xiao-Ming He, Xin Zhao, W. Zou
semanticscholar +1 more source
Normalized solutions of fractional Choquard equation with critical nonlinearity
Differential and Integral Equations, 2023Zhaosheng Feng, Xiao-Ming He, Yu-Xi Meng
semanticscholar +1 more source