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A Class of Fractional p-Laplacian Integrodifferential Equations in Banach Spaces [PDF]
Abstract and Applied Analysis, 2013 We study a class of nonlinear fractional integrodifferential equations with p-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractional p-Laplacian equations ...
Yiliang Liu, Liang Lu
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The extremal solution for the fractional Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2013 We study the extremal solution for the problem $(- )^s u= f(u)$ in $ $, $u\equiv0$ in $\R^n\setminus $, where $ >0$ is a parameter and $s\in(0,1)$. We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded
Xavier Ros‐Oton, Joaquim Serra
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Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian [PDF]
Journal of Function Spaces and Applications, 2013 We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut ...
Ya-ling Li, Shi-you Lin
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An extension problem for the CR fractional Laplacian [PDF]
Advances in Mathematics, 2014 We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre.
Rupert L. Frank +3 more
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Maximum principles for Laplacian and fractional Laplacian with critical integrability
The Journal of Geometric Analysis, 2019 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider $-\Delta u(x)+c(x)u(x)\geq 0$ in $B_1$ where $c(x)\in L^{p}(B_1)$, $B_1\subset \mathbf{R}^n$. As is known that $p=\frac{n}{2}$
Lü, Yingshu
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On fractional $p$-Laplacian problems with weight [PDF]
Differential and Integral Equations, 2015 10 ...
Raquel Lehrer +2 more
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Radial symmetry for a generalized nonlinear fractional p-Laplacian problem
Nonlinear Analysis, 2021 This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p ...
Wenwen Hou +3 more
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Fractal and Fractional, 2023 The fractional Laplacian operator is a very important fractional operator that is often used to describe several anomalous diffusion phenomena. In this paper, we develop some numerical schemes, including a finite difference scheme and finite volume ...
Junjie Wang, Shoucheng Yuan, Xiao Liu
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On the fractional Laplacian of variable order [PDF]
Fractional Calculus and Applied Analysis, 2022 Abstract We present a novel definition of variable-order fractional Laplacian on $${\mathbb {R}}^n$$ R n
Darve, Eric +4 more
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Fractional Laplacians on ellipsoids
Mathematics in Engineering, 2021 6 pictures, 27 ...
Abatangelo N., Jarohs S., Saldana A.
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