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A survey on variational characterizations for nonlinear eigenvalue problems. (English) Zbl 07436835

Summary: 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 generalizations of these principles to families of linear, self-adjoint operators depending continuously on a scalar in a real interval.

MSC:

65-XX Numerical analysis
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
47A52 Linear operators and ill-posed problems, regularization
47A75 Eigenvalue problems for linear operators
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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References:

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