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Finite Element Approximation of the Minimal Eigenvalue of a Nonlinear Eigenvalue Problem [PDF]

Lobachevskii Journal of Mathematics, 2018
© 2018, Pleiades Publishing, Ltd. The problem of finding the minimal eigenvalue corresponding to a positive eigenfunction of the nonlinear eigenvalue problem for the ordinary differential equation with coefficients depending on a spectral parameter is ...
S I Solov'Ev, P S Solov'Ev, Solov'Ev S I
exaly   +1 more source

A nonlinear eigenvalue optimization problem: Optimal potential functions

Nonlinear Analysis: Real World Applications, 2018
In this paper we study the following optimal shape design problem: Given an open connected set Ω⊂RN and a positive number A∈(0,|Ω|), find a measurable subset D⊂Ω with |D|=A such that the minimal eigenvalue of −div(ζ(λ,x)∇u)+αχDu=λu in Ω, u=0 on ∂Ω, is as
Pedro R S Antunes, Seyyed Abbas Mohammadi, Heinrich Voß   +2 more
exaly   +1 more source

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A nonlinear eigenvalue problem

Theoretical and Mathematical Physics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chankaev, M. Kh., Shabat, A. B.
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Algorithms for the Nonlinear Eigenvalue Problem

SIAM Journal on Numerical Analysis, 1973
The following nonlinear eigenvalue problem is studied : Let $T(\lambda )$ be an $n \times n$ matrix, whose elements are analytical functions of the complex number $\lambda $. We seek $\lambda $ and vectors x and y, such that $T(\lambda )x = 0$, and $y^H T(\lambda ) = 0$.Several algorithms for the numerical solution of this problem are studied.
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On a nonlinear eigenvalue problem

Integral Equations and Operator Theory, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gasanov, M., Cesur, Y.
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On a Nonlinear Eigenvalue Problem

1987
Publisher Summary This chapter presents the nonlinear boundary value problem, where Ω is a simply connected and bounded domain in R2 with smooth boundary. The chapter discusses the possibility of the connectedness between the branch of minimal solutions and that of Weston–Moseley's large solutions.
Ken'ichi Nagasaki, Takashi Suzuki
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Exact solution of a nonlinear eigenvalue problem

Physical Review A, 1986
We show that Shastry's exact solution of a nonlinear eigenvalue problem in one dimension can be recovered by a method which is familiar in the theory of nonlinear ordinary differential equations.
, Romeiras, , Rowlands
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On nonlinear eigenvalue problems

Forum Mathematicum, 1992
Summary: The aim of this paper is to establish the existence of an infinite sequence of eigenvalues and eigenfunctions \((\mu_ m,u_ m)\) for the problem \(A(u)+C(u)=\mu B(u)\), where \(A\), \(B\) and \(C\) are mappings from a real infinite dimensional Banach space \(X\) into its dual \(X^*\) and \(\mu\) is a real parameter. This is proved using minimax
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On the numerical solution of nonlinear eigenvalue problems

Computing, 1995
Let \(A(\lambda, \rho)\) be an \(n \times n\) matrix which is nonlinear in \(\lambda\) and \(\rho\). Consider the nonlinear eigenvalue problem \[ A(\lambda (\rho), \rho) x (\rho) = 0, \quad y (\rho)^T A(\lambda (\rho), \rho) = 0^T \] together with some desirable scaling schemes for the right and left eigenvectors \(x\) and \(y\).
L. Andrew, K. E. Chu, Peter Lancaster
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On a non-linear eigenvalue problem

USSR Computational Mathematics and Mathematical Physics, 1984
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