Results 51 to 60 of about 5,262 (196)
Lyapunov-type inequalities for the fractional p-sub-Laplacian [PDF]
, 2020 In this paper we study the fractional Dirichlet p-sub-Laplacian in a Haar measurable set on homogeneous Lie groups. We show analogues of the fractional Sobolev and Hardy inequalities and we also present a Lyapunov-type inequality for the fractional p-sub-
Suragan, Durvudkhan, Kassymov, Aidyn
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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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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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Overdetermined problems with fractional laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2015 Added a missing assumption (1.3) in Theorem 1.1 and Theorem 1.2, which is used in the proof of Lemma 4 ...
Fall, Mouhamed Moustapha, Jarohs, Sven
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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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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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The parabolic p-Laplacian with fractional differentiability [PDF]
IMA Journal of Numerical Analysis, 2020 Abstract We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space–time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskiǐ spaces and therefore cover situations when the (gradient of the) solution has only fractional ...
Breit, Dominic +3 more
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Riesz potential versus fractional Laplacian [PDF]
, 2014 This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied.
Laleg-Kirati, Taous-Meriem +4 more
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On the Laplacian and fractional Laplacian in an exterior domain
Advances in Differential Equations, 2012 We see that the generalized Fourier transform due to A.G. Ramm for the case of $n=3$ space dimensions remains valid, with some modifications, for all space dimensions $n\ge 2$. We use the resulting spectral representation of the exterior Laplacian to study exterior problems. In particular the Fourier splitting method developed by M.E.
Kosloff, Leonardo, Schonbek, Tomas
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