Results 111 to 120 of about 446 (156)

Existence and mass collapse behavior of standing waves for Choquard equation with rotation

We are concerned with the existence and mass collapse behavior of standing waves with the prescribed mass for the Choquard equation with rotation, which serves as a model to describe the Bose–Einstein condensate of nonrelativistic particles with rotation
Su, Yu, Feng, Zhaosheng
core   +1 more source

Existence and nonexistence of nontrivial solutions for Choquard type equations

Electronic Journal of Differential Equations, 2016
In this article, we consider the nonlocal problem $$ -\Delta u+u=q(x)\Big(\int_{\mathbb{R}^N}\frac{q(y)|u(y)|^p}{|x-y|^{N-\alpha}}dy \Big)|u|^{p-2}u,\quad x\in \mathbb{R}^N, $$ where $N\geq 3$, $\alpha\in (0,N)$, $\frac{N+\alpha}{N}
Tao Wang
doaj  

Existence and stability of standing waves for the Choquard equation with partial confinement

, 2020
In this paper we study the existence and orbital stability of the Choquard equation with partial confinement. This type equation originates from Fröhlich and Pekar's model of the polaron, where free electrons in an ionic lattice interact with phonons ...
Xiao, Lu, Geng, Qiuping, Zhu, Maochun, Wang, Jun   +3 more
core  

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

Positive solutions with prescribed mass for a planar Choquard equation

We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser.
Romani, Giulio, Huan, Ling
core  

Existence of normalized solutions to Choquard equation with general mixed nonlinearities

We study the existence of normalized solutions to the following Choquard equation with $F$ being a Berestycki-Lions type function \begin{equation*} \begin{cases} -Δu+λu=(I_α\ast F(u))f(u),\quad \text{in}\ \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=ρ^2, \
Zhu, Meiling, Li, Xinfu
core  

A guide to the Choquard equation [PDF]

Journal of Fixed Point Theory and Applications, 2016
39 ...
Vitaly Moroz, Jean Van Schaftingen, Moroz Vitaly   +2 more
exaly   +7 more sources

High energy solutions of the Choquard equation

Discrete and Continuous Dynamical Systems, 2018
The present paper is concerned with the existence of positive high energy solution of the Choquard equation. Under certain assumptions, the ground state of Choquard equation can not be achieved. However, by global compactness analysis, we prove that there exists a positive high energy solution.
Daomin Cao
exaly   +4 more sources

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Saddle solutions for the Choquard equation II

Nonlinear Analysis, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Zhi-Qiang, Xia, Jiankang
openaire   +2 more sources

Quasilinear Choquard equation with critical exponent

Journal of Mathematical Analysis and Applications, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu Su, Hongxia Shi
exaly   +2 more sources