The subspace iteration method for nonlinear eigenvalue problems occurring in the dynamics of structures with viscoelastic elements

2021 ◽  
Vol 254 ◽  
pp. 106571
Author(s):  
Magdalena Łasecka-Plura ◽  
Roman Lewandowski
Keyword(s):  
Iteration Method ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problems ◽  
Subspace Iteration ◽  
Nonlinear Eigenvalue

scholarly journals A Subspace Iteration Algorithm for Fredholm Valued Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Christian Engström ◽  
Luka Grubišić
Keyword(s):  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Spectral Component ◽  
Contour Integration ◽  
Iteration Algorithm ◽  
Nonlinear Eigenvalue Problems ◽  
Infinite Dimensional ◽  
Subspace Iteration ◽  
Fredholm Theorem ◽  
Nonlinear Eigenvalue

We present an algorithm for approximating an eigensubspace of a spectral component of an analytic Fredholm valued function. Our approach is based on numerical contour integration and the analytic Fredholm theorem. The presented method can be seen as a variant of the FEAST algorithm for infinite dimensional nonlinear eigenvalue problems. Numerical experiments illustrate the performance of the algorithm for polynomial and rational eigenvalue problems.

MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Eigenvalue Problems ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.

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