Variational Principles for Eigenvalues of Nonlinear Eigenproblems

  • Heinrich VossEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)


Variational principles are very powerful tools when studying self-adjoint linear operators on a Hilbert space \(\mathcal{H}\). Bounds for eigenvalues, comparison theorems, interlacing results and monotonicity of eigenvalues can be proved easily with these characterizations, to name just a few. In this paper we consider generalization of these principles to families of linear, self-adjoint operators depending continuously on a scalar in a real interval.


Variational Principle Essential Spectrum Nonlinear Eigenvalue Problem Operator Pencil Extreme Eigenvalue 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of MathematicsHamburg University of TechnologyHamburgGermany

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