Abstract
We consider an equation of the form Au+N(u)=λu in a Hilbert space and assume that the nonlinearity N is reproducing relative to a known sequence of vectors. Under this assumption the Rayleigh-Ritz-Galerkin approximations lead to a simple class of nonlinear algebraic eigenvalue problems.
In a general variational case we show that Lusternik-Schnirelmann critical values of Rayleigh-Ritz-Galerkin problems provide upper bounds to those of the original problem. Lower bounds are constructed in the case N(u)=B*(Bu)3.
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The author would like to thank the European Research Office for their assistance in this research.
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Bazley, N.W. Approximation of operators with reproducing nonlinearities. Manuscripta Math 18, 353–369 (1976). https://doi.org/10.1007/BF01270496
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DOI: https://doi.org/10.1007/BF01270496