Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics [PDF]
, 2013 We consider a semilinear elliptic problem [- \Delta u + u = (I_\alpha \ast \abs{u}^p) \abs{u}^{p - 2} u \quad\text{in (\mathbb{R}^N),}] where (I_\alpha) is a Riesz potential and (p>1).
Moroz, Vitaly, Van Schaftingen, Jean
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Ground state solutions for non-autonomous fractional Choquard equations [PDF]
Nonlinearity, 2016 15 ...
Chen, Yan-Hong, Liu, Chungen
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Exponential Scattering for a Damped Hartree Equation
Fractal and Fractional, 2023 This note studies the linearly damped generalized Hartree equation iu˙−(−Δ)su+iau=±|u|p−2(Jγ∗|u|p)u ...
Talal Alharbi +2 more
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Kirchhoff Equations with Choquard Exponential Type Nonlinearity Involving the Fractional Laplacian [PDF]
Acta Applicandae Mathematicae, 2021 23 ...
Goyal, Sarika, Mukherjee, Tuhina
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Advanced Nonlinear Studies, 2022 In this paper, we consider the following critical fractional magnetic Choquard equation: ε2s(−Δ)A∕εsu+V(x)u=εα−N∫RN∣u(y)∣2s,α∗∣x−y∣αdy∣u∣2s,α∗−2u+εα−N∫RNF(y,∣u(y)∣2)∣x−y∣αdyf(x,∣u∣2)uinRN,\begin{array}{rcl}{\varepsilon }^{2s}{\left(-\Delta )}_{A ...
Jin Zhen-Feng +2 more
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Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains [PDF]
, 2012 We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schroedinger--Newton equation. We show that for some values of
Agmon +40 more
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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).
Ghimenti, MARCO GIPO +2 more
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The Choquard Equation with Weighted Terms and Sobolev‐Hardy Exponent
Journal of Function Spaces, Volume 2018, Issue 1, 2018., 2018 We study a nonlinear Choquard equation with weighted terms and critical Sobolev‐Hardy exponent. We apply variational methods and Lusternik‐Schnirelmann category to prove the multiple positive solutions for this problem.
Yanbin Sang +3 more
wiley +1 more source
Coulomb system equivalent to the energy spectrum of the Calogero-Sutherland-Moser (CSM) model [PDF]
, 2018 The purpose of this paper is to prove an equivalence between the energy spectrum of the CSM model and the electrostatic energy of a one-dimensional lattice of quantized point charges interacting via Coulomb potential with Dirichlet boundary ...
Choquard, Ph
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Cooperative Ring Exchange and Quantum Melting of Vortex Lattices in Atomic Bose-Einstein Condensates [PDF]
, 2003 Cooperative ring-exchange is suggested as a mechanism of quantum melting of vortex lattices in a rapidly-rotating quasi two dimensional atomic Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al. [Phys. Rev. Lett. {\bf 56}, 873 (
Dung-Hai Lee +20 more
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