Results 11 to 20 of about 1,494,768 (123)

Ground State Solutions of Fractional Choquard Problems with Critical Growth

Fractal and Fractional, 2023
In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained.
Jie Yang, Hongxia Shi
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Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity

Mathematics, 2019
In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non ...
Huxiao Luo, Shengjun Li, Chunji Li
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Concentration phenomena for a fractional Choquard equation with magnetic field [PDF]

Dynamics of Partial Differential Equations, 2018
We consider the following nonlinear fractional Choquard equation $$ \varepsilon^{2s}(-\Delta)^{s}_{A/\varepsilon} u + V(x)u = \varepsilon^{\mu-N}\left(\frac{1}{|x|^{\mu}}*F(|u|^{2})\right)f(|u|^{2})u \mbox{ in } \mathbb{R}^{N}, $$ where $\varepsilon>0 ...
V. Ambrosio
semanticscholar   +2 more sources

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N≥3, F represents the primitive function of f,  f∈CR;R is a function that fulfils the general ...
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao   +3 more
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Multiple Normalized Solutions to a Choquard Equation Involving Fractional p-Laplacian in ℝ^N

Fractal and Fractional
In this paper, we study the existence of multiple normalized solutions for a Choquard equation involving fractional p-Laplacian in RN. With the help of variational methods, minimization techniques, and the Lusternik–Schnirelmann category, the existence ...
Xin Zhang, Sihua Liang
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Nodal solutions for a fractional Choquard equation

Journal of Mathematical Analysis and Applications, 2018
In this paper, we study the existence of nodal solutions for the following fractional Choquard equation ( − △ ) α u + u = ∫ R N | u ( z ) | p | x − z | μ d z | u ( x ) | p − 2 u ( x ) , x ∈ R N , where 0 μ 2 α N and 2 N − μ N − 1 p 2 N − μ N − 2 α with α
Wei Zhang, Xian Wu
exaly   +2 more sources

Ground state solutions for asymptotically periodic fractional Choquard equations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2019
This paper is dedicated to studying the following fractional Choquard equation \begin{equation*} (-\triangle)^s u+V(x)u=\left(\int_{\mathbb{R}^N}\frac{Q(y)F(u(y))}{|x-y|^\mu}\mathrm{d}y\right)Q(x)f(u), \qquad u\in H^s(\mathbb{R}^{N}), \end{equation*
Sitong Chen, Xianhua Tang
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Concentrating Solutions of the Fractional (p,q)-Choquard Equation with Exponential Growth [PDF]

Analysis and Applications
This article deals with the following fractional $(p,q)$-Choquard equation with exponential growth of the form: $$\varepsilon^{ps}(-\Delta)_{p}^{s}u+\varepsilon^{qs}(-\Delta)_q^su+ Z(x)(|u|^{p-2}u+|u|^{q-2}u)=\varepsilon^{\mu-N}[|x|^{-\mu}*F(u)]f(u) \ \ \
Yueqiang Song, Xue-Qi Sun, D. Repovš
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Normalized ground states for the lower critical fractional Choquard equation with a focusing local perturbation

Discrete and Continuous Dynamical Systems - Series S, 2023
Chun-Lei Tang, Ziheng Zhang
exaly   +2 more sources

Multiple concentrating solutions for a fractional (p, q)-Choquard equation [PDF]

Advanced Nonlinear Studies
We focus on the following fractional (p, q)-Choquard problem: (−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=1|x|μ*F(u)f(u) in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0 in RN, $\begin{cases}{\left(-{\Delta}\right)}_{p}^{s}u+{\left(-{\Delta}\right)}_{q}^{s}u+V\left(\varepsilon ...
Ambrosio Vincenzo
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