Results 11 to 20 of about 628 (105)
On fractional Choquard equations [PDF]
Mathematical Models and Methods in Applied Sciences, 2014 We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.Comment: revised version, 22 ...
Bongers A. +8 more
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Fractional Choquard equation with critical nonlinearities [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2017 In this article, we study the Brezis-Nirenberg type problem of nonlinear Choquard equation involving a fractional Laplacian \[ (-\De)^s u = \left( \int_{\Om}\frac{|u|^{2^*_{ ,s}}}{|x-y|^ }\mathrm{d}y \right)|u|^{2^*_{ ,s}-2}u +\la u \; \text{in } \Om,\] where $\Om $ is a bounded domain in $\mathbb R^n$ with Lipschitz boundary, $\la $ is a real ...
Mukherjee, T., Sreenadh, K.
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Nonlocal perturbations of the fractional Choquard equation
Advances in Nonlinear Analysis, 2017 We study the ...
Singh Gurpreet
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Advances in Nonlinear Analysis, 2022 This paper is concerned with existence and concentration properties of ground-state solutions to the following fractional Choquard equation with indefinite potential: (−Δ)su+V(x)u=∫RNA(εy)∣u(y)∣p∣x−y∣μdyA(εx)∣u(x)∣p−2u(x),x∈RN,{\left(-\Delta )}^{s}u+V ...
Zhang Wen, Yuan Shuai, Wen Lixi
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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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Multiple concentrating solutions for a fractional (p, q)-Choquard equation
Advanced Nonlinear StudiesWe focus on the following fractional (p, q)-Choquard problem: (−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=1|x|μ*F(u)f(u) in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0 in RN, $\begin{cases}{\left(-{\Delta}\right)}_{p}^{s}u+{\left(-{\Delta}\right)}_{q}^{s}u+V\left(\varepsilon ...
Ambrosio Vincenzo
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Concentration phenomena for a fractional Choquard equation with magnetic field [PDF]
Dynamics of Partial Differential Equations, 2018 We consider the following nonlinear fractional Choquard equation $$ \varepsilon^{2s}(-\Delta)^{s}_{A/\varepsilon} u + V(x)u = \varepsilon^{\mu-N}\left(\frac{1}{|x|^{\mu}}*F(|u|^{2})\right)f(|u|^{2})u \mbox{ in } \mathbb{R}^{N}, $$ where $\varepsilon>0 ...
Ambrosio, Vincenzo
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Saddle solutions for the fractional Choquard equation [PDF]
Zeitschrift für angewandte Mathematik und Physik, 2022 We study the saddle solutions for the fractional Choquard equation \begin{align*} (- )^{s}u+ u=(K_ \ast|u|^{p})|u|^{p-2}u, \quad x\in \mathbb{R}^N \end{align*} where $s\in(0,1)$, $N\geq 3$ and $K_ $ is the Riesz potential with order $ \in (0,N)$. For every Coxeter group $G$ with rank $1\leq k\leq N$ and $p\in[2,\frac{N+ }{N-2s})$, we construct a ...
Ying-Xin Cui, Jiankang Xia
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Regularity results for Choquard equations involving fractional p‐Laplacian
Mathematische Nachrichten, 2023 AbstractIn this paper, first we address the regularity of weak solution for a class of p‐fractional Choquard equations: where is a smooth bounded domain, and such that , and is a continuous function with at most critical growth condition (in the sense of the Hardy–Littlewood–Sobolev inequality) and F is its primitive.
Biswas, Reshmi, Tiwari, Sweta
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On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=00,v= on ∂Ω,where Ω ⊂ ℝN is a bounded domain with a smooth boundary, 0 < α < N, 0 < β < N, and F is the primitive of f, similarly for G.
Wenbo Wang +3 more
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