Results 61 to 70 of about 628 (105)

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
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Limit profiles and the existence of bound-states in exterior domains for fractional Choquard equations with critical exponent

Advances in Nonlinear Analysis
This article is devoted to studying the existence of positive solutions to the following fractional Choquard equation: (−Δ)su+u=∫Ω∣u(y)∣p∣x−y∣N−αdy∣u∣p−2u+ε∫Ω∣u(y)∣2α,s*∣x−y∣N−αdy∣u∣2α,s*−2u,inΩ,u=0,onRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+u=
Ye Fumei, Yu Shubin, Tang Chun-Lei
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Remarks on the nonlinear fractional Choquard equation

Fractional Calculus and Applied Analysis
Abstract We analyze the following doubly nonlocal nonlinear elliptic problem: $$\begin{aligned} \left\{ \begin{array}{ll} (-\varDelta )^{s}u+\omega u=(I_{\alpha }*F(u)) F'(u) \text{ in } \mathbb {R}^{N}, \\ u\in H^{s}(\mathbb {R}^{N}), \end{array} \right. \end{aligned}$$
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Multiplicity of solutions to a nonlocal Choquard equation involving fractional magnetic operators and critical exponent

Electronic Journal of Differential Equations, 2016
In this article, we study the multiplicity of solutions to a nonlocal fractional Choquard equation involving an external magnetic potential and critical exponent, namely, $$\displaylines{ (a+b[u]_{s,A}^2)(-\Delta)_A^su+V(x)u =\int_{\mathbb{R}^N ...
Fuliang Wang, Mingqi Xiang
doaj  

Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities

Electronic Journal of Differential Equations, 2019
In this work, we establish the existence of solutions for the nonlinear nonlocal system of equations involving the fractional Laplacian, \begin{gather*} \begin{aligned} (-\Delta)^s u & = au+bv+\frac{2p}{p+q}\int_{\Omega}\frac{|v(y)|^q}{|x-y|^\mu}dy|
Yang Yang, Qian Yu Hong, Xudong Shang
doaj  

Symmetry and Nonexistence of Positive Solutions for Fractional Choquard Equations

, 2017
This paper is devoted to study the following Choquard equation \begin{eqnarray*}\left\{ \begin{array}{lll} (-\triangle)^{ /2}u=(|x|^{ -n}\ast u^p)u^{p-1},~~~&x\in R^n, u\geq0,\,\,&x\in R^n, \end{array} \right.
Ma, Pei, Zhang, Jihui
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Fractional p -Kirchhoff equation with Sobolev and Choquard singular nonlinearities

Complex Variables and Elliptic Equations
25 ...
R. B. Assunção, O. H. Miyagaki, R. F. S. Siqueira   +2 more
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Semi-classical states for fractional Choquard equations with decaying potentials

Communications in Contemporary Mathematics
This paper deals with the following fractional Choquard equation: [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text], [Formula: see text] is the fractional Laplacian, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] is a Riesz potential, [Formula: see text] is an external potential.
Yinbin Deng, Shuangjie Peng, Xian Yang
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Asymptotic decay of solutions for sublinear fractional Choquard equations

Nonlinear Analysis
Goal of this paper is to study the asymptotic behaviour of the solutions of the following doubly nonlocal equation $$(-Δ)^s u + μu = (I_α*F(u))f(u) \quad \hbox{on $\mathbb{R}^N$}$$ where $s \in (0,1)$, $N\geq 2$, $α\in (0,N)$, $μ>0$, $I_α$ denotes the Riesz potential and $F(t) = \int_0^t f(τ) d τ$ is a general nonlinearity with a sublinear growth in
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A novel method for approximate solution of two point non local fractional order coupled boundary value problems. [PDF]

PLoS One
Tadoummant L, Khalil H, Echarggaoui R, Aljohani S, Mlaiki N.   +4 more
europepmc   +1 more source