Results 81 to 90 of about 446 (156)

Ground state solutions and decay estimation of Choquard equation with critical exponent and Dipole potential

, 2023
In this paper, we study a class of Choquard equations with critical exponent and Dipole potential. We prove the existence of radial ground state solutions for Choquard equations by using the refined Sobolev inequality with the Morrey norm, and show that ...
Su, Yu, Feng, Zhaosheng
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A priori estimates for a critical Schrodinger-Newton equation

Electronic Journal of Differential Equations, 2013
Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent.
Marcelo M. Disconzi
doaj  

Existence, symmetry, and regularity of ground states of a nonlinear Choquard equation in the hyperbolic space

Advances in Nonlinear Analysis
In this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
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On critical Choquard equation with potential well

Discrete and Continuous Dynamical Systems, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shen, Zifei, Gao, Fashun, Yang, Minbo
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Ground state solutions for a (p,q)-Choquard equation with a general nonlinearity [PDF]

In this paper, we study the existence of ground state solutions for the following (p,q)-Choquard equation: −Δpu−Δqu+|u|p−2u+|u|q−2u=(Iα⁎F(u))f(u) in RN, where 2≤
Ambrosio V., Isernia T.
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Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth

Advances in Nonlinear Analysis
We study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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The Choquard logarithmic equation involving a nonlinearity with exponential growth

, 2022
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. We prove

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Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

Advances in Nonlinear Analysis
In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently ...
Luo Huxiao, Zhang Dingliang, Xu Yating
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Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

Boundary Value Problems, 2019
In this paper, we consider the sharp thresholds of blow-up and global existence for the nonlinear Schrödinger–Choquard equation i ψ t + Δ ψ = λ 1 | ψ | p 1 ψ + λ 2 ( I α ∗ | ψ | p 2 ) | ψ | p 2 − 2 ψ .
Yongbin Wang, Binhua Feng
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Standing waves for Choquard equation with noncritical rotation

Advances in Nonlinear Analysis
We investigate the existence and stability of standing waves with prescribed mass c>0c\gt 0 for Choquard equation with noncritical rotation in Bose-Einstein condensation. Then, we consider the mass collapse behavior of standing waves, the ratio of energy
Mao Yicen, Yang Jie, Su Yu
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