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NONLINEAR MULTIPARAMETER EIGENVALUE PROBLEMS

NONLINEAR MULTIPARAMETER EIGENVALUE PROBLEMS
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A nonlinear eigenvalue problem

Theoretical and Mathematical Physics, 2008
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Chankaev, M. Kh., Shabat, A. B.
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Nonlinear Multiparameter Eigenvalue Problems in Aeroelasticity

International Journal of Structural Stability and Dynamics, 2019
In this work, we devise solution algorithms for nonlinear multiparameter eigenvalue problems arising in the analysis of aeroelastic flutter. Two iterative algorithms are devised, as well as a restriction method for simplifying the system behavior away from the desired flutter points. The algorithms are tested on a sectional model and on the Goland wing.
Pons, Arion, Gutschmidt, Stefanie
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Nonlinear Eigenvalue Problems on Infinite Intervals

SIAM Journal on Mathematical Analysis, 1983
This paper considers the nonlinear eigenvalue problems of boundary value problems for ordinary differential equations of the form (1) \(y'=t^{\alpha}A(t,\lambda)y\), \(1\leq t-1\), (2) \(B(\lambda)y(1)=0\), \((3)\quad y\in C([1,\infty]):\Leftrightarrow y\in C([1,\infty])\) and \(\lim_{t\to \infty}y(t)\) exists where y is an n- vector and A(t,\(\lambda)\
Markowich, Peter A., Weiss, Richard
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Nonlinear Elliptic Eigenvalue Problems

1992
As a further application of the direct methods of the calculus of variations let us discuss a special class of nonlinear eigenvalue problems. As far as the technical framework is concerned, we proceed here as in our treatment of nonlinear boundary value problems in Chap.
Philippe Blanchard, Erwin Brüning
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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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Sturm Sequences for Nonlinear Eigenvalue Problems

SIAM Journal on Mathematical Analysis, 1989
The author wants to treat Sturm-Liouville eigenvalue problems, where the coefficients depend nonlinearly on a parameter. For this purpose the classical theorems on Sturm sequences are reconsidered from a more axiomatic point of view. This covers these nonlinear eigenvalue problems, and also their finite-element approximation, which result in ...
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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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Nonlinear eigenvalue topology optimization for structures with frequency-dependent material properties

Mechanical Systems and Signal Processing, 2022
Quhao Li, Suguang Dou, Shutian Liu
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