Results 81 to 90 of about 1,353 (146)

On Nodal Solutions of the Nonlinear Choquard Equation

Advanced Nonlinear Studies, 2019
Abstract This paper deals with the general Choquard equation -
Changfeng Gui, Hui Guo
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Dynamics of blow-up solutions for the Schrödinger–Choquard equation

Boundary Value Problems, 2018
In this paper, we study the dynamics of blow-up solutions for the nonlinear Schrödinger–Choquard equation iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. $$i\psi_{t}+\Delta \psi =\lambda_{1}\vert \psi \vert ^{p_{1}}\psi +\lambda_{2}\bigl(I _{\alpha }\ast \vert ...
Cunqin Shi, Kun Liu
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Nonlinear Choquard equations on hyperbolic space

Opuscula Mathematica, 2022
In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the hyperbolic space \(\mathbb{B}^N\), where \(\Delta_{\mathbb{B}^{N}}\) denotes the Laplace-Beltrami ...
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Multiple normalized solutions for Choquard equation involving the biharmonic operator and competing potentials in

Bulletin of Mathematical Sciences
This paper is concerned with the existence of multiple normalized solutions for a class of Choquard equation involving the biharmonic operator and competing potentials in [Formula: see text]: Δ2u+V(𝜀x)u=λu+G(𝜀x)(Iμ∗F(u))f(u)in ℝN,∫ℝN|u|2dx=c2, where ...
Shuaishuai Liang, Jiaying Ma, Shaoyun Shi, Yueqiang Song   +3 more
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Solutions to discrete nonlinear Kirchhoff–Choquard equations

Bulletin of the Malaysian Mathematical Sciences Society
18 ...
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Ground state solutions for asymptotically periodic fractional Choquard equations

Electronic Journal of Qualitative Theory of Differential Equations, 2019
This paper is dedicated to studying the following fractional Choquard equation \begin{equation*} (-\triangle)^s u+V(x)u=\left(\int_{\mathbb{R}^N}\frac{Q(y)F(u(y))}{|x-y|^\mu}\mathrm{d}y\right)Q(x)f(u), \qquad u\in H^s(\mathbb{R}^{N}), \end{equation*
Sitong Chen, Xianhua Tang
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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
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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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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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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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