Results 61 to 70 of about 33,013 (283)
Numerical Methods for the Fractional Laplacian: a Finite Difference-quadrature Approach
, 2014 The fractional Laplacian $(-\Delta)^{\alpha/2}$ is a non-local operator which depends on the parameter $\alpha$ and recovers the usual Laplacian as $\alpha \to 2$.
Huang, Yanghong, Oberman, Adam
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A note on the existence and multiplicity of solutions for sublinear fractional problems
Boundary Value Problems, 2017 In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u ...
Yongqiang Fu
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Critical Concave Convex Ambrosetti–Prodi Type Problems for Fractional 𝑝-Laplacian
Advanced Nonlinear Studies, 2020 In this paper, we consider a class of critical concave convex Ambrosetti–Prodi type problems involving the fractional p-Laplacian operator. By applying the linking theorem and the mountain pass theorem as well, the interaction of the nonlinearities with ...
Bueno H. P. +3 more
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Non degeneracy of the bubble in the critical case for non local equations
, 2013 We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional ...
Davila, Juan +2 more
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IEEE Access, 2019 Hadamard fractional calculus theory has made many scholars enthusiastic and excited because of its special logarithmic function integral kernel. In this paper, we focus on a class of Caputo-Hadamard-type fractional turbulent flow model involving $p(t)$ -
Guotao Wang +3 more
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The trace fractional Laplacian and the mid-range fractional Laplacian
Nonlinear AnalysisIn this paper we introduce two new fractional versions of the Laplacian. The first one is based on the classical formula that writes the usual Laplacian as the sum of the eigenvalues of the Hessian. The second one comes from looking at the classical fractional Laplacian as the mean value (in the sphere) of the 1-dimensional fractional Laplacians in ...
Julio D. Rossi, Jorge Ruiz-Cases
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Eigenvalues for systems of fractional $p$-Laplacians [PDF]
Rocky Mountain Journal of Mathematics, 2018 We study the eigenvalue problem for a system of fractional $p-$Laplacians, that is, $$ \begin{cases} (- _p)^r u = \dfrac p|u|^{ -2}u|v|^ &\text{in } ,\vspace{.1cm} (- _p)^s u = \dfrac p|u|^ |v|^{ -2}v &\text{in } , u=v=0 &\text{in } ^c=\R^N\setminus . \end{cases} $$ We show that there is a first (smallest) eigenvalue that
Pezzo, Leandro M. Del, Rossi, Julio D.
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, 2016 We consider the fractional Laplacian operator $(-\Delta)^s$ (let $ s \in (0,1) $) on Euclidean space and investigate the validity of the classical integration-by-parts formula that connects the $ L^2(\mathbb{R}^d) $ scalar product between a function and ...
Muratori, Matteo
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Advanced Science, EarlyView.Upon ischemia/reperfusion‐induced iron overload condition, neurons and astrocytes exhibit similar oxidative stress changes but opposite alterations in endogenous antioxidant defense mechanisms, leading to divergent ferroptotic outcomes. The iron deposition and neuronal loss are increased within the perilesional cortex of stroke patients ...
Yi Guo +17 more
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AIMS Mathematics, 2023 In this manuscript, the main objective is to analyze the existence, uniqueness, (EU) and stability of positive solution for a general class of non-linear fractional differential equation (FDE) with fractional differential and fractional integral boundary
Kirti Kaushik +3 more
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