Results 51 to 60 of about 101,180 (174)
Lower bounds for fractional Laplacian eigenvalues [PDF]
Communications in Contemporary Mathematics, 2014 In this paper, we investigate eigenvalues of fractional Laplacian (–Δ)α/2|D, where α ∈ (0, 2], on a bounded domain in an n-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which improves some results due to Yildirim Yolcu and Yolcu in [Estimates for the sums of eigenvalues of the fractional Laplacian on a ...
Lingzhong Zeng, He-Jun Sun, Guoxin Wei
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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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A mixed operator approach to peridynamics
Mathematics in Engineering, 2023 In the present paper we propose a model describing the nonlocal behavior of an elastic body using a peridynamical approach. Indeed, peridynamics is a suitable framework for problems where discontinuities appear naturally, such as fractures, dislocations,
Federico Cluni +4 more
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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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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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On the fractional Dunkl Laplacian [PDF]
arXiv, 2021 In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem for the fractional Dunkl Laplacian as ...
arxiv
Getting Acquainted with the Fractional Laplacian [PDF]
, 2019 updated version, 72 pages, 12 ...
Abatangelo N., Valdinoci E.
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Overdetermined problems with fractional laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2015 Let $N\geq 1$ and $s\in (0,1)$. In the present work we characterize bounded open sets $ $ with $ C^2$ boundary (\textit{not necessarily connected}) for which the following overdetermined problem \begin{equation*} ( - )^s u = f(u) \text{ in $ $,} \qquad u=0 \text{ in $\mathbb{R}^N\setminus $,} \qquad(\partial_ )_s u=Const. \text{ on $\partial $}
Sven Jarohs, Mouhamed Moustapha Fall
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Fractional conformal Laplacians and fractional Yamabe problems [PDF]
Analysis & PDE, 2013 Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar.
González Nogueras, María del Mar +1 more
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Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials
Advanced Nonlinear Studies, 2017 In this paper, we consider a class of Schrödinger equations involving fractional Laplacian and indefinite potentials. By modifying the definition of the Nehari–Pankov manifold, we prove the existence and asymptotic behavior of least energy solutions.
Tang Zhongwei, Wang Lushun
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