Nonlinear eigenvalue problems and contour integrals

Nonlinear eigenvalue problems and contour integrals

Beyn’s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a Hankel tensor. A numerical example shows that the choice of the filter function is very important, particularly with respect to where it is positioned in the complex plane.

Nonlinear Eigenvalue Problems

Heinrich Voss Hamburg University of Technology 115.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-2 115.2 Analytic matrix functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-3 115.3 Variational Characterization of Eigenvalues . . . . . . . . 115-7 115.4 General Rayleigh Functionals . . . . . . . . . . . . . . . . . . . ...

Solving nonlinear eigenvalue problems

Two-parametric nonlinear eigenvalue problems

Eigenvalue problems of the form x′′ = −λf(x) + μg(x−), (i), x(0) = 0, x(1) = 0, (ii) are considered, where x and x− are the positive and negative parts of x respectively. We are looking for (λ, μ) such that the problem (i), (ii) has a nontrivial solution. This problem generalizes the famous Fuč́ık problem for piece-wise linear equations. In our considerations functions f and g may be nonlinear f...

Orlicz Spaces and Nonlinear Elliptic Eigenvalue Problems

Nonlinear elliptic differential equations of order m acting in a space of m dimensions often occupy a special position in more general theories. In this paper we shall study one aspect of this situation. The nonlinear problem under consideration will be the variational approach to eigenvalue problems for nonlinear elliptic partial differential equations as developed by the author in [l], [2], [...