Results 51 to 60 of about 628 (105)

Liouville Type Theorem For A Nonlinear Neumann Problem [PDF]

, 2016
Consider the following nonlinear Neumann problem \[ \begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on }\partial\mathbb{R}_ ...
Xiang, Changlin
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Existence and stability of standing waves for coupled nonlinear Hartree type equations

, 2019
We study existence and stability of standing waves for coupled nonlinear Hartree type equations \[ -i\frac{\partial}{\partial t}\psi_j=\Delta \psi_j+\sum_{k=1}^m \left(W\star |\psi_k|^p \right)|\psi_j|^{p-2}\psi_j, \] where $\psi_j:\mathbb{R}^N\times ...
Bhattarai, Santosh
core   +1 more source

Critical Fractional Choquard–Kirchhoff Equation with p-Laplacian and Perturbation Terms on the Heisenberg Group

Fractal and Fractional
In this paper, we are interested in a class of critical fractional Choquard–Kirchhoff equations with p-Laplacian on the Heisenberg group. By employing several critical point theorems, we obtain the existence and multiplicity of nontrivial solutions under
Xueyan Ma, Sihua Liang, Yueqiang Song
doaj   +1 more source

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
doaj   +1 more source

Semiclassical states for fractional Choquard equations with critical growth

Communications on Pure & Applied Analysis, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Hui, Wang, Jun, Zhang, Fubao
openaire   +3 more sources

Groundstates for nonlinear fractional Choquard equations with general nonlinearities

, 2014
There is a serious mistake in the proof that we can not cover the gap at this ...
Shen, Zifei, Gao, Fashun, Yang, Minbo
openaire   +2 more sources

Existence of solutions for fractional p-Kirchhoff type equations with a generalized Choquard nonlinearities

, 2018
In this article, we establish the existence of solutions to the fractional $p-$Kirchhoff type equations with a generalized Choquard nonlinearities without assuming the Ambrosetti-Rabinowitz ...
Chen, Wenjing
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NOTE ON SOME FRACTIONAL BI-INHOMOGENEOUS SCHRODINGER-CHOQUARD EQUATIONS [PDF]

, 2020
In the subcritical energy case, local well-posedness is established in the radial energy space for a class of fractional inhomogeneous Choquard equations. The best constant of a Gagliardo-Nirenberg type inequality is obtained. Moreover, a sharp threshold of global existence versus blow-up dichotomy is obtained for mass super-critical and energy ...
openaire   +1 more source

Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity

, 2017
This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy-Littlewood-Sobolev inequality \begin{equation*} \left\{ \begin{split ...
Giacomoni, J., Mukherjee, Tuhina, Sreenadh, K.   +2 more
core  

Nonlocal Hardy type inequalities with optimal constants and remainder terms

, 2012
Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha}{2}}\dif x \dif y \le ...
Moroz, Vitaly, Van Schaftingen, Jean
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