Results 61 to 70 of about 1,353 (146)
Coron Problem for Nonlocal Equations Involving Choquard Nonlinearity
Advanced Nonlinear Studies, 2019 Abstract We consider the following Choquard equation: {
Divya Goel +2 more
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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 +4 more
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A guide to the Choquard equation [PDF]
Journal of Fixed Point Theory and Applications, 2016 39 ...
Moroz, Vitaly, Van Schaftingen, Jean
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Soliton dynamics for the generalized Choquard equation
, 2013 We investigate the soliton dynamics for a class of nonlinear Schr\"odinger equations with a non-local nonlinear term. In particular, we consider what we call {\em generalized Choquard equation} where the nonlinear term is $(|x|^{\theta-N} * |u|^p)|u|^{p ...
Bonanno, Claudio +3 more
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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,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat +2 more
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On the critical Choquard-Kirchhoff problem on the Heisenberg group
Advances in Nonlinear Analysis, 2022 In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
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Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, we consider the following quasilinear p⟶⋅‐elliptic problems with flux boundary conditions of the type −∑i=1N∂/∂xiaix,∂u/∂xi+bxupMx−2u=f1x,u−sgnug1x in Ω,∑i=1Naix,∂u/∂xiνi=cxuqx−2u+f2x,u−sgnug2x on ∂Ω.. Using the Fountain theorem and dual Fountain theorem, we prove the existence and multiplicity of solutions for a given problem, subject ...
Ahmed Ahmed +2 more
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Choquard equations with recurrent potentials
Advances in Nonlinear AnalysisAbstract In this article, we are concerned with the existence of nontrivial solutions to the Choquard equation − Δ u + α
Ding, Hui-Sheng +3 more
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Weighted Choquard Equation Perturbed with Weighted Nonlocal Term [PDF]
Differential Equations and Dynamical Systems, 2021 AbstractWe investigate the following problem $$\begin{aligned} -\mathrm{div}(v(x)|\nabla u|^{m-2}\nabla u)+V(x)|u|^{m-2}u= \left( |x|^{-\theta }*\frac{|u|^{b}}{|x|^{\alpha }}\right) \frac{|u|^{b-2}}{|x|^{\alpha }}u+\lambda \left( |x|^{-\gamma }*\frac{|u|^{c}}{|x|^{\beta }}\right) \frac{|u|^{c-2}}{|x|^{\beta }}u \quad \text { in }{\mathbb {R}}^{N}, \end{
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Normalized solutions for the Choquard equation with potential and combined nonlinearities
Advances in Nonlinear AnalysisIn this paper, we study multiple normalized solutions for the following Choquard equation:
Xing Wenjun, Suo Hongmin, Lei Chunyu
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