Abstract
A functional is given which generalizes the Rayleigh quotient to eigenvalue problems for linear operators where the eigenvalue parameter appears nonlinearly. Particular emphasis is given to the development of perturbation-type results for eigenvalues and characteristic values which generalize the classical results. Applications are made to eigenvalue and characteristic value problems for integral and matrix operators and to the critical length problem for integral operators. Both symmetric and nonsymmetric operators are treated.
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References
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Additional Bibliography
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Communicated by R. E. Kalaba
The author would like to acknowledge the work of Gloria Golberg in the preparation of this paper.
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Golberg, M.A. A generalized Rayleigh quotient for eigenvalue problems nonlinear in the parameter. J Optim Theory Appl 11, 146–158 (1973). https://doi.org/10.1007/BF00935880
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DOI: https://doi.org/10.1007/BF00935880