Results 111 to 120 of about 112,078 (333)
Error investigation of finite element approximation for a nonlinear Sturm–Liouville problem
Учёные записки Казанского университета: Серия Физико-математические науки, 2017 A positive definite differential eigenvalue problem with coefficients depending nonlinearly on the spectral parameter has been studied. The differential eigenvalue problem is formulated as a variational eigenvalue problem in a Hilbert space with bilinear
A.A. Samsonov +2 more
doaj
Uniform level set estimates for ground state eigenfunctions [PDF]
arXiv, 2017 We study the behaviour of the first eigenfunction of the Dirichlet Laplacian on a planar convex domain near its maximum. We show that the eccentricity and orientation of the superlevel sets of the eigenfunction stabilise as they approach the maximum, uniformly with respect to the eccentricity of the domain itself.
arxiv
Nodal sets of Robin and Neumann eigenfunctions [PDF]
arXiv, 2018 We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the interior nodal sets is obtained for Robin eigenfunctions in the smooth domain. For the analytic domain, the sharp upper bounds of the interior nodal sets was shown for Robin eigenfunctions. More
arxiv
On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori
, 2015 In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tori. We present two results.
Léna, Corentin
core
Narrow Linewidth Laser Based on Extended Topological Interface States in 1D Photonic Crystals
Laser &Photonics Reviews, EarlyView.This work introduces a novel 1D‐TISE‐PhC semiconductor laser structure achieving uniform photon distribution, reduced linewidth (126 kHz), robust single‐mode performance (SMSR up to 50 dB), precise wavelength control, and tolerance to fabrication variations, demonstrated experimentally in an eight‐channel array.
Xiao Sun +8 more
wiley +1 more source
When is the first eigenfunction for the clamped plate equation of fixed sign?
Electronic Journal of Differential Equations, 2001 It is known that the first eigenfunction of the clamped plate equation, $Delta^2 varphi = lambda varphi$ in $Omega$ with $varphi=frac{partial}{partial n}varphi=0$ on $partialOmega$, is not necessarily of fixed sign.
Guido Sweers
doaj
International Journal of Mathematics and Mathematical Sciences, 2009 We consider the following eigenvalue problem: −Δ𝑢+𝑓(𝑢)=𝜆𝑢, 𝑢=𝑢(𝑥), 𝑥∈𝐵={𝑥∈ℝ3∶|𝑥|0, 𝑢||𝑥|=1=0, where 𝑝 is an arbitrary fixed parameter and 𝑓 is an odd smooth function.
Peter Zhidkov
doaj +1 more source
On series of Walsh eigenfunctions [PDF]
Proceedings of the American Mathematical Society, 1951 and the boundary conditions u(O) = 0, u(1) = 0, the function g(x) being assumed continuous on 0 ? x < 1. He used the asymptotic formula for the kth eigenfunction (1) uk(x) = (2)1/2 [sin k7rx + (1/k)4k(x)], | k(X) | _ C. Comparing series of these functions with corresponding series of the functions (2) Uk(X) = (2)1/2 sin kirx, he proved that if a ...
openaire +2 more sources
An eigenvalue problem for the infinity-Laplacian
Electronic Journal of Differential Equations, 2013 In this work, we study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction.
Tilak Bhattacharya, Leonardo Marazzi
doaj
Characterization of Besov spaces with dominating mixed smoothness by differences
Mathematische Nachrichten, EarlyView.Abstract Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of differences is provided. Applications to random fields, like Gaussian fields and the stochastic heat equation, are discussed, based on a Kolmogorov ...
Paul Nikolaev +2 more
wiley +1 more source