On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$
Applications of Mathematics, Tome 26 (1981) no. 3, pp. 211-240.

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The Collatz method of twosided eigenvalue estimates was extended by K. Rektorys in his monography Variational Methods to the case of differential equations of the form $Au - \lambda Bu=0$ with elliptic operators. This method requires to solve, successively, certain boundary value problems. In the case of partial differential equations, these problems are to be solved approximately, as a rule, and this is the source of further errors. In the work, it is shown how to estimate these additional errors, or how to avoid them by a proper modification of the method. At the same time, some results of their own interest are derived.
DOI : 10.21136/AM.1981.103913
Classification : 35P15, 49G05, 65N15, 65N25, 65N30
Mots-clés : Collatz method; twosided eigenvalue estimates; elliptic operators 
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Rektorys, Karel; Vospěl, Zdeněk. On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$. Applications of Mathematics, Tome 26 (1981) no. 3, pp. 211-240. doi : 10.21136/AM.1981.103913. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1981.103913/

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