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The Hardy potential and eigenvalue problems [PDF]
Opuscula Mathematica, 2011 We establish the existence of principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We consider the Dirichlet and Neumann boundary conditions.
Jan Chabrowski
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Rectangular eigenvalue problems
Advances in Computational Mathematics, 2022 AbstractOften the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m ≫ n collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems.
Hashemi, B +2 more
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Two-parametric nonlinear eigenvalue problems
Electronic Journal of Qualitative Theory of Differential Equations, 2008 Eigenvalue problems of the form $x'' = -\lambda f(x^+) + \mu g(x^-),$ $\quad (i),$ $x(0) = 0, \; x(1) = 0,$ $\quad (ii)$ are considered, where $x^+$ and $x^-$ are the positive and negative parts of $x$ respectively.
Armands Gritsans, Felix Sadyrbaev
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Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems
SIAM Journal of Scientific Computing, 2014 Daniel Kressner +2 more
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Quadratic Eigenvalue Problems [PDF]
Mathematische Nachrichten, 1995 We consider the quadratic eigenvalue problem \[ (\mu^2 R+\mu S+T) y= 0\tag{1} \] with selfadjoint operators \(R\), \(S\) and \(T\) in the Hilbert space \({\mathcal G}\). The operator \(S\) is supposed to be ``large'' with respect to the operators \(R\) and \(T\). For simplicity we assume that \(R\) and \(T\) have bounded inverses. If, additionally, \(S\
Ćurgus, Branko, Najman, Branko
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Supersolutions to nonautonomous Choquard equations in general domains
Advances in Nonlinear Analysis, 2023 We consider the nonlocal quasilinear elliptic problem: −Δmu(x)=H(x)((Iα*(Qf(u)))(x))βg(u(x))inΩ,-{\Delta }_{m}u\left(x)=H\left(x){(\left({I}_{\alpha }* \left(Qf\left(u)))\left(x))}^{\beta }g\left(u\left(x))\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0 ...
Aghajani Asadollah, Kinnunen Juha
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Product Eigenvalue Problems [PDF]
SIAM Review, 2005 Summary: Many eigenvalue problems are most naturally viewed as product eigenvalue problems. The eigenvalues of a matrix \(A\) are wanted, but \(A\) is not given explicitly. Instead it is presented as a product of several factors: \(A = A_{k}A_{k-1}\dots A_{1}\). Usually more accurate results are obtained by working with the factors rather than forming \
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The nonlinear eigenvalue problem [PDF]
Acta Numerica, 2017 Nonlinear eigenvalue problems arise in a variety of science and engineering applications, and in the past ten years there have been numerous breakthroughs in the development of numerical methods. This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a ...
Stefan Güttel, Françoise Tisseur
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Existence of solutions for 4p-order PDES with Neumann boundary conditions
Moroccan Journal of Pure and Applied Analysis, 2023 In this work, we study the existence of at least one non decreasing sequence of nonnegative eigenvalues for the problem: {Δ2pu=λm(x)u in Ω,∂u∂v=∂(Δu)∂v=…=∂(Δ2p-1u)∂v=0 on ∂Ω.\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u ...
Moradi N. +3 more
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Nonlinear nonhomogeneous Neumann eigenvalue problems
Electronic Journal of Qualitative Theory of Differential Equations, 2015 We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero.
Pasquale Candito +2 more
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