Second Eigenfunctions of Nonlinear Eigenvalue Problems

Nonlinear Eigenvalue Problems of Schrr Odinger Type Admitting Eigenfunctions with given Spectral Characteristics

The following work is an extension of our recent paper 10]. We still deal with nonlinear eigenvalue problems of the form A 0 y + B(y)y = y (*) in a real Hilbert space H with a semi-bounded self-adjoint operator A 0 , while for every y from a dense subspace X of H, B(y) is a symmetric operator. The left{hand side is assumed to be related to a certain auxiliary functional , and the associated lin...

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...

Sign-preserving of principal eigenfunctions in P1 finite element approximation of eigenvalue problems of second-order elliptic operators

This talk is concerned with the P1 finite element approximation of the eigenvalue problem of second-order elliptic operators subject to the Dirichlet boundary condition. The focus is on the preservation of basic properties of the principal eigenvalue and eigenfunctions of continuous problems. We shall show that when the stiffness matrix is an irreducible M-matrix, the algebraic eigenvalue probl...