Results 1 to 10 of about 1,067 (48)
On Aharonov–Bohm Operators with Two Colliding Poles [PDF]
Advanced Nonlinear Studies, 2017 We consider Aharonov–Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.
Abatangelo Laura +2 more
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On Duclos–Exner’s conjecture about waveguides in strong uniform magnetic fields
Forum of Mathematics, Sigma, 2023 We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition on the width and the curvature of the strip ensuring the existence of the discrete spectrum in the strong magnetic field ...
Enguerrand Bon-Lavigne +3 more
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Conformal upper bounds for the eigenvalues of the p‐Laplacian
Journal of the London Mathematical Society, Volume 104, Issue 5, Page 2128-2147, December 2021., 2021 Abstract In this note we present upper bounds for the variational eigenvalues of the p‐Laplacian on smooth domains of complete n‐dimensional Riemannian manifolds and Neumann boundary conditions, and on compact (boundaryless) Riemannian manifolds. In particular, we provide upper bounds in the conformal class of a given metric for 1
Bruno Colbois, Luigi Provenzano
wiley +1 more source
Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces
Open Mathematics, 2021 In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space (M,⟨,⟩,e−ϕdv)\left(M,\langle ,\rangle ,{e}^{-\phi }{\rm{d}}v), with nonnegative weighted Ricci curvature Ricϕ≥0{{\rm{Ric}}}^{\phi }\ge 0 for
Hou Lanbao +3 more
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Estimates for eigenvalues of the Neumann and Steklov problems
Advances in Nonlinear Analysis, 2023 We prove Li-Yau-Kröger-type bounds for Neumann-type eigenvalues of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which ...
Du Feng +4 more
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Eigenfunctions in Finsler Gaussian solitons
Open Mathematics, 2023 Gaussian solitons are important examples in the theory of Riemannian measure space. In the first part, we explicitly characterize the first eigenfunctions of the drift Laplacian in a Gaussian shrinking soliton, which shows that apart from each coordinate
Liu Caiyun, Yin Songting
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Dirichlet problems involving the Hardy-Leray operators with multiple polars
Advances in Nonlinear Analysis, 2023 Our aim of this article is to study qualitative properties of Dirichlet problems involving the Hardy-Leray operator ℒV≔−Δ+V{{\mathcal{ {\mathcal L} }}}_{V}:= -\Delta +V, where V(x)=∑i=1mμi∣x−Ai∣2V\left(x)={\sum }_{i=1}^{m}\frac{{\mu }_{i}}{{| x-{A}_{i}| }
Chen Huyuan, Chen Xiaowei
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Equitable colourings of Borel graphs
Forum of Mathematics, Pi, 2021 Hajnal and Szemerédi proved that if G is a finite graph with maximum degree $\Delta $ , then for every integer $k \geq \Delta +1$ , G has a proper colouring with k colours in which every two colour classes differ in size at most by $1$ ;
Anton Bernshteyn, Clinton T. Conley
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On the solutions to p-Poisson equation with Robin boundary conditions when p goes to +∞
Advances in Nonlinear Analysis, 2022 We study the behaviour, when p→+∞p\to +\infty , of the first p-Laplacian eigenvalues with Robin boundary conditions and the limit of the associated eigenfunctions.
Amato Vincenzo +3 more
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Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order
Advances in Nonlinear Analysis, 2022 In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully obtain a general inequality for
Du Feng +3 more
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