Results 41 to 50 of about 1,494,768 (123)
Time fractional advection-dispersion equation [PDF]
, 2003 A time fractional advection-dispersion equation is obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order α ...
Anh, Vo +3 more
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Asymptotic behavior of ground states for a fractional Choquard equation with critical growth
AIMS Mathematics, 2021 In this paper, we are concerned with the following fractional Choquard equation with critical growth: $ (-\Delta)^s u+\lambda V(x)u = (|x|^{-\mu} \ast F(u))f(u)+|u|^{2^*_s-2}u \; \hbox{in}\; \mathbb{R}^N, $ where $ s\in (0, 1) $, $ N > 2s $, $ \mu\in (0,
Xianyong Yang, Qing Miao
semanticscholar +1 more source
Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.This paper is concerned with the positive solutions to a fractional‐order system with Hartree‐type nonlinearity and its equivalent integral system. We firstly use the regularity lifting lemma to obtain the integrability and smoothness of the solutions.
Yu-Cheng An +2 more
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Existence of Multiple Positive Solutions for Choquard Equation with Perturbation [PDF]
, 2015 This paper is concerned with the following Choquard equation with perturbation: -Δu+V(x)u=(1/|x|α∗|u|p)|u|p-2u+g(x), u∈H1(RN), where N≥3, α∈(0,N), and 2-(α/N)
Jun Wang, Tao Xie, Lu Xiao
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Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator [PDF]
Opuscula MathematicaIn this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_ ...
Nidhi Nidhi, Konijeti Sreenadh
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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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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
wiley +1 more source
The Riesz-Bessel Fractional Diffusion Equation [PDF]
, 2004 This paper examines the properties of a fractional diffusion equation defined by the composition of the inverses of the Riesz potential and the Bessel potential. The first part determines the conditions under which the Green function of this equation is
Anh, Vo V., McVinish, Ross S.
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Numerical simulation of the fractional Langevin equation [PDF]
, 2012 In this paper, we study the fractional Langevin equation, whose derivative is in Caputo sense. By using the derived numerical algorithm, we obtain the displacement and the mean square displacement which describe the dynamic behaviors of the fractional ...
Li, Changpin +5 more
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