Results 41 to 50 of about 264,054 (242)
Nonnegative solutions of nonlinear fractional Laplacian equations [PDF]
, 2020 The study of reaction-diffusion equations involving nonlocal diffusion operators has recently flourished. The fractional Laplacian is an example of a nonlocal diffusion operator which allows long-range interactions in space, and it is therefore important
Hollifield, Elliott Z. +1 more
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Boundary value problems for the fractional Pauli operator: spectral methods and convergence analysis [PDF]
Mathematics and Computational SciencesThis paper investigates boundary value problems for the fractional Pauli operator on a finite square domain, addressing a significant gap in the literature where such problems have not been previously studied.
Yusif Gasimov, Aynura Aliyeva
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Mathematics, 2022 In this paper, by using fixed-point theorems, the existence and uniqueness of positive solutions to a class of four-point impulsive fractional differential equations with p-Laplacian operators are studied. In addition, three examples are given to justify
Limin Chu +3 more
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The Spatially Variant Fractional Laplacian
Fractional Calculus and Applied Analysis, 2023 We introduce a definition of the fractional Laplacian $(-Δ)^{s(\cdot)}$ with spatially variable order $s:Ω\to [0,1]$ and study the solvability of the associated Poisson problem on a bounded domain $Ω$. The initial motivation arises from the extension results of Caffarelli and Silvestre, and Stinga and Torrea; however the analytical tools and approaches
Andrea N. Ceretani, Carlos N. Rautenberg
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Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities
Advances in Nonlinear Analysis, 2022 In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}.
Tao Mengfei, Zhang Binlin
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Fractional Laplacian system involving doubly critical nonlinearities in $\mathbb{R}^N$
Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this article, we are interested in a fractional Laplacian system in $\mathbb{R}^N$, which involves critical Sobolev-type nonlinearities and critical Hardy–Sobolev-type nonlinearities.
Li Wang, Binlin Zhang, Haijin Zhang
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Existence of Multiple Weak Solutions to a Discrete Fractional Boundary Value Problem
Axioms, 2023 The existence of at least three weak solutions to a discrete fractional boundary value problem containing a p-Laplacian operator and subject to perturbations is proved using variational methods. Some applications of the main results are presented.
Shahin Moradi +2 more
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Mellin definition of the fractional Laplacian [PDF]
, 2023 It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is ...
Pagnini, G., Runfola, C.
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ON (GLOBAL) UNIQUE CONTINUATION PROPERTIES OF THE FRACTIONAL DISCRETE LAPLACIAN [PDF]
, 2023 We study various qualitative and quantitative (global) unique continuation prop- erties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation ...
Fernández-Bertolin, A. +2 more
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A Class of Fractional p-Laplacian Integrodifferential Equations in Banach Spaces
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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