Results 1 to 10 of about 1,494,768 (123)

Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation

Advances in Nonlinear Analysis, 2023
In this article, we study the fractional critical Choquard equation with a nonlocal perturbation: (−Δ)su=λu+α(Iμ*∣u∣q)∣u∣q−2u+(Iμ*∣u∣2μ,s*)∣u∣2μ,s*−2u,inRN,{\left(-{\Delta })}^{s}u=\lambda u+\alpha \left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{q}){| u|
Lan Jiali, He Xiaoming, Meng Yuxi
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Existence and concentration of ground-states for fractional Choquard equation with indefinite potential

Advances in Nonlinear Analysis, 2022
This paper is concerned with existence and concentration properties of ground-state solutions to the following fractional Choquard equation with indefinite potential: (−Δ)su+V(x)u=∫RNA(εy)∣u(y)∣p∣x−y∣μdyA(εx)∣u(x)∣p−2u(x),x∈RN,{\left(-\Delta )}^{s}u+V ...
Zhang Wen, Yuan Shuai, Wen Lixi
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Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

Advances in Nonlinear Analysis, 2020
In this paper, we study the singularly perturbed fractional Choquard ...
Yang Zhipeng, Zhao Fukun
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Multiplicity and Concentration Results for a Fractional Choquard Equation via Penalization Method [PDF]

Potential Analysis, 2017
This paper is devoted to the study of the following fractional Choquard equation ε2s(−Δ)su+V(x)u=εμ−N1|x|μ∗F(u)f(u)inℝN,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}
Vincenzo Ambrosio
exaly   +3 more sources

Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

Advances in Nonlinear Analysis, 2020
In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard ...
Binhua Feng, Chen Ruipeng, Liu Jiayin
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Regularity for critical fractional Choquard equation with singular potential and its applications

Advances in Nonlinear Analysis
We study the following fractional Choquard equation (−Δ)su+u∣x∣θ=(Iα*F(u))f(u),x∈RN,{\left(-\Delta )}^{s}u+\frac{u}{{| x| }^{\theta }}=({I}_{\alpha }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N⩾3N\geqslant 3, s∈12,1s\in \left ...
Liu Senli, Yang Jie, Su Yu
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Nonlocal perturbations of the fractional Choquard equation

Advances in Nonlinear Analysis, 2017
We study the ...
Singh Gurpreet
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Sign-Changing Solutions for the Fractional Choquard Equation

Axioms
We study a class of fractional Choquard equation with continuous potential. This equation is a doubly nonlocal problem which has two nonlocal term: fractional Laplacian operator and convolution term. Using variaotional metheod and some estimates, we give
Ying-Xin Cui, Qiaoyan Li
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On nonlinear fractional Choquard equation with indefinite potential and general nonlinearity

Boundary Value Problems, 2023
In this paper, we consider a class of fractional Choquard equations with indefinite potential ( − Δ ) α u + V ( x ) u = [ ∫ R N M ( ϵ y ) G ( u ) | x − y | μ d y ] M ( ϵ x ) g ( u ) , x ∈ R N , $$ (-\Delta )^{\alpha}u+V(x)u= \biggl[ \int _{{\mathbb{R ...
Fangfang Liao, Fulai Chen, Shifeng Geng, Dong Liu   +3 more
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On nodal solutions of the fractional Choquard equation

Journal of Mathematical Analysis and Applications, 2021
In this paper, we study the following fractional Choquard equation ( − Δ ) s u + u = ( K α ⁎ | u | p ) | u | p − 2 u , x ∈ R N . Using variational methods on Nehari manifold, we prove that there is an odd solution for this equation under an energy ...
Ying-Xin Cui
exaly   +2 more sources