Results 51 to 60 of about 446 (156)

Normalized Ground State Solutions for Nonautonomous Choquard Equations

Frontiers of Mathematics, 2023
In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-Δu-λu=\left(\frac{1}{|x|^μ}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \int_{\mathbb{R}^{N}}|u|^{2}dx=c,\quad u\in H^1(\mathbb{R}^N,\mathbb{R}),$$ where $c>0$, $0< ...
Luo, Huxiao, Wang, Lushun
openaire   +3 more sources

Global existence and blowup conditions for 调和solutions of an inhomogeneous Choquard equation

四川大学学报. 自然科学版, 2022
In this paper, we mainly study the global existence and blowup conditions for the solutions of an inhomogeneous Choquard equation when the initial data is above the ground state"s mass-energy.
HE Qiao-Ling, HUANG Juan
doaj  

Existence of stable standing waves for the Schrödinger–Choquard equation

Boundary Value Problems, 2018
In this paper, by variational methods and the profile decomposition of bounded sequences in H1 $H^{1}$ we study the existence of stable standing waves for the Schrödinger–Choquard equation with an L2 $L^{2}$-critical nonlinearity. Our results extend some
Kun Liu, Cunqin Shi
doaj   +1 more source

Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco, Yanghong Huang, Zeng Liu, Vitaly Moroz   +3 more
wiley   +1 more source

MULTIPLE POSITIVE SOLUTIONS AND BIFURCATION FOR AN EQUATION RELATED TO CHOQUARD’S EQUATION [PDF]

Proceedings of the Edinburgh Mathematical Society, 2003
AbstractIn this paper we study the existence of multiple positive solutions and the bifurcation problem for the following equation:$$ -\Delta u+u=\biggl(\int_{\mathbb{R}^3}\frac{|u(y)|^2}{|x-y|}\,\mathrm{d}y\biggr)u+\mu f(x),\quad x\in\mathbb{R}^3, $$where $f(x)\in H^{-1}(\mathbb{R}^3)$, $f(x)\geq0$, $f(x)\not\equiv0$.
Küpper, Tassilo, Zhang, Zhengjie, Xia, Hongqiang   +2 more
openaire   +2 more sources

On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn

Analysis and Geometry in Metric Spaces
This article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving ...
Liang Sihua, Pucci Patrizia, Song Yueqiang, Sun Xueqi   +3 more
doaj   +1 more source

Regularity and Classification of Solutions to Fractional‐Order Systems With Hartree‐Type Nonlinearities

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
This paper is concerned with the positive solutions to a fractional‐order system with Hartree‐type nonlinearity and its equivalent integral system. We firstly use the regularity lifting lemma to obtain the integrability and smoothness of the solutions.
Yu-Cheng An, Guai-Qi Tian, Douglas R. Anderson   +2 more
wiley   +1 more source

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N ≥ 3, F represents the primitive function of f, f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao, Kang-Jia Wang   +4 more
wiley   +1 more source

Planar Choquard equations with critical exponential reaction and Neumann boundary condition

Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.
Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat, Vicenţiu D. Rădulescu, K. Sreenadh   +2 more
wiley   +1 more source

The Choquard logarithmic equation involving a nonlinearity with exponential growth [PDF]

, 2020
In the present work we are concerned with the Choquard Logarithmic equation $-\Delta u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u)$ in $\mathbb{R}^2$, for $ a>0 $, $ \lambda >0 $ and a nonlinearity $f$ with exponential critical growth.
Miyagaki, Olímpio Hiroshi, Böer, Eduardo de Souza   +1 more
core   +1 more source