Eldar Sh. Mamedov, “Variational principle for two-parameter spectral problem under left definiteness condition”, Proc. of Institute of mathematics and mechanics, 2015, Volume 41, Issue 2,Pages <nobr>124

Variational principle for two-parameter spectral problem under left definiteness condition

Eldar Sh. Mamedov^ab

^a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
^b Azerbaijan Technical University, Baku

Abstract: In the paper we consider two-parameter spectral problem
\begin{equation*} \begin{cases} {\lambda _{1} K_{r1} \varphi _{r} +\lambda _{2} K_{r2} \varphi _{r} =\varphi _{r} ,\quad \varphi _{r} \in H_{r} }, \\ {r=1,2} \end{cases} \end{equation*}
with compact self-adjoint operators in Hilbert space under left definiteness condition. The analog of the variational principle was obtained for the two-parameter spectral problem.

MSC: 47J22, 47A10, 47A75

Received: 08.10.2015
Accepted: 30.11.2015

Language: English