Results 51 to 60 of about 1,216,221 (148)
Least action nodal solutions for the quadratic Choquard equation [PDF]
, 2016 We prove the existence of a minimal action nodal solution for the quadratic Choquard equation (Formula presented), where Iα is the Riesz potential of order α ∈ (0,N).
Vitaly Moroz +4 more
core +1 more source
Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities
Advanced Nonlinear Studies, 2021 In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential.
Shen Yansheng
doaj +1 more source
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
Multiple solutions for a quasilinear Choquard equation with critical nonlinearity
Open Mathematics, 2021 In the present work, we are concerned with the multiple solutions for quasilinear Choquard equation with critical nonlinearity in RN{{\mathbb{R}}}^{N}.
Li Rui, Song Yueqiang
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,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
MULTIPLE POSITIVE SOLUTIONS AND BIFURCATION FOR AN EQUATION RELATED TO CHOQUARD’S EQUATION [PDF]
Proceedings of the Edinburgh Mathematical Society, 2003 AbstractIn this paper we study the existence of multiple positive solutions and the bifurcation problem for the following equation:$$ -\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 +2 more
openaire +2 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
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 +2 more
wiley +1 more source
On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn
Analysis and Geometry in Metric SpacesThis 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 +3 more
doaj +1 more source
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