Results 71 to 80 of about 1,353 (146)

Standing waves with a critical frequency for nonlinear Choquard equations

, 2016
In this paper, we study the nonlocal Choquard equation $$ -\varepsilon^2 \Delta u_\varepsilon + V u_\varepsilon= (I_\alpha * |u_\varepsilon|^p)|u_\varepsilon|^{p-2}u_\varepsilon $$ where $N\geq 1$, $I_\alpha$ is the Riesz potential of order $\alpha \in ...
Van Schaftingen, Jean, Xia, Jiankang
core   +1 more source

A nontrivial solution for a nonautonomous Choquard equation with general nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2022
With the help of the monotonicity trick, a nonautonomous Choquard equations with general nonlinearity is studied and a nontrivial solution is obtained.
Ling Ding, Jiu Liu, Yan-Xiang Yuan
doaj   +1 more source

Non-linear bi-harmonic Choquard equations

Communications on Pure and Applied Analysis, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Existence of positive solutions to the nonlinear Choquard equation with competing potentials

Electronic Journal of Differential Equations, 2018
This article concerns the existence of positive solutions of the nonlinear Choquard equation $$ -\Delta u+a(x)u=b(x)\Big(\frac{1}{|x|}*|u|^2\Big)u,\quad u\in H^{1}({\mathbb R}^3), $$ where the coefficients a and b are positive functions such that
Jun Wang, Mengmeng Qu, Lu Xiao
doaj  

Global dynamics of the parabolic Choquard equation with asymptotically linear nonlinearity

Journal of Inequalities and Applications
This article investigates the global dynamics of the semilinear parabolic Choquard equation ∂ t u ( x , t ) − Δ u ( x , t ) + u ( x , t ) = ( I α ∗ | u ( ⋅ , t ) | p ) ( x ) | u ( x , t ) | p − 2 u ( x , t ) + f ( u ( x , t ) ) , ( x , t ) ∈ R N × ( 0 , ∞
Salah Boulaaras
doaj   +1 more source

Can quantum systems succumb to their own (gravitational) attraction?

, 2014
The gravitational interaction is generally considered to be too weak to be easily submitted to systematic experimental investigation in the quantum, microscopic, domain.
Colin, Samuel, Durt, Thomas, Willox, Ralph   +2 more
core   +1 more source

Nonlocal perturbations of the fractional Choquard equation

Advances in Nonlinear Analysis, 2017
We study the ...
Singh Gurpreet
doaj   +1 more source

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
doaj   +1 more source

Semi-classical states for the Choquard equation [PDF]

Calculus of Variations and Partial Differential Equations, 2014
28 pages, updated ...
Moroz, Vitaly, van Schaftingen, Jean
openaire   +4 more sources

Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System [PDF]

, 2014
A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \[ \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta V=Q^{2}, & \text{
Xiang, Changlin
core