Results 51 to 60 of about 264,054 (242)
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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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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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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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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Generic properties of eigenvalues of the fractional Laplacian [PDF]
, 2023 We consider the Dirichlet eigenvalues of the fractional Laplacian, related to a smooth bounded domain. We prove that there exists an arbitrarily small perturbation of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian are
Micheletti A. M. +3 more
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Maximum Principles for Laplacian and Fractional Laplacian with Critical Integrability
The Journal of Geometric Analysis, 2023 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider the critical cases for Laplacian with zero order term and first order term. It is well known that for the Laplacian with zero order term $-Δ+c(x)$ in $B_1$, $c(x)\in L^p(B_1)$($B_1\subset \mathbf{R}^n$), the critical case for
Congming Li, Yingshu Lü
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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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Preserving Motor Features by Alternative Re‐Referencing to Remove Heart Artifact on the Stentrode
Advanced Science, EarlyView.Endovascular brain‐computer interfaces record neural activity from within cerebrovasculature, at the expense of electrocardiogram contamination. Band‐limited independent component analysis separates this heart‐based artifact from task‐relevant neural activity in each frequency band, enabling the reconstruction of cleaner neural recordings without the ...
Ariel K. Feldman +11 more
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