TY  - JOUR
ID  - Boyko2018
LB  - Boyko2018
AU  - Boyko, Olga
AU  - Martynyuk, Olga
AU  - Pivovarchik, Vyacheslav
TI  - On spectra of quadratic operator pencils with rank one gyroscopic linear part
ST  - On spectra of quadratic operator pencils with rank one gyroscopic linear part
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 4
SP  - 483
EP  - 500
DO  - https://doi.org/10.7494/OpMath.2018.38.4.483
UR  - https://doi.org/10.7494/OpMath.2018.38.4.483
AB  - The spectrum of a selfadjoint quadratic operator pencil of the form \(\lambda^2M-\lambda G-A\) is investigated where \(M\geq 0\), \(G\geq 0\) are bounded operators and \(A\) is selfadjoint bounded below is investigated. It is shown that in the case of rank one operator \(G\) the eigenvalues of such a pencil are of two types. The eigenvalues of one of these types are independent of the operator \(G\). Location of the eigenvalues of both types is described. Examples for the case of the Sturm-Liouville operators \(A\) are given.
KW  - quadratic operator pencil
KW  - gyroscopic force
KW  - eigenvalues
KW  - algebraic multiplicity
SN  - 1232-9274
ER  -