On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$

Rektorys, Karel, and Vospěl, Zdeněk. "On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$." Aplikace matematiky 26.3 (1981): 211-240. <http://eudml.org/doc/15197>.

@article{Rektorys1981,
abstract = {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.},
author = {Rektorys, Karel, Vospěl, Zdeněk},
journal = {Aplikace matematiky},
keywords = {Collatz method; twosided eigenvalue estimates; elliptic operators; Collatz method; twosided eigenvalue estimates; elliptic operators},
language = {eng},
number = {3},
pages = {211-240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$},
url = {http://eudml.org/doc/15197},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Rektorys, Karel
AU - Vospěl, Zdeněk
TI - On a method of two-sided eigenvalue estimates for elliptic equations of the form $Au-\lambda Bu=0$
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 3
SP - 211
EP - 240
AB - 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.
LA - eng
KW - Collatz method; twosided eigenvalue estimates; elliptic operators; Collatz method; twosided eigenvalue estimates; elliptic operators
UR - http://eudml.org/doc/15197
ER -