Nonlinear eigenvalue Neumann problems with discontinuities

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

Nonlinear Eigenvalue Problems with Specified Eigenvalues

This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T , we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed algebraic multiplicities. While the usual resolvent norm addresses this question for a single eigenvalue of multiplicity one, the general sett...

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...

Multiple Solutions for Strongly Resonant Nonlinear Elliptic Problems with Discontinuities

We examine a nonlinear strongly resonant elliptic problem driven by the p-Laplacian and with a discontinuous nonlinearity. We assume that the discontinuity points are countable and at them the nonlinearity has an upward jump discontinuity. We show that the problem has at least two nontrivial solutions without using a multivalued interpretation of the problem as it is often the case in the liter...