A two-parameter eigenvalue problem for a class of block-operator matrices

TL;DR

This paper investigates a symmetric block operator spectral problem involving two spectral parameters, establishing localization theorems for pair-eigenvalues and exploring their connections to non-self-adjoint spectral problems.

Contribution

It introduces localization theorems for pair-eigenvalues in a two-parameter eigenvalue problem and relates these findings to non-self-adjoint spectral problems.

Findings

Localization theorems for pair-eigenvalues

Relations to non-self-adjoint spectral problems

Conditions under which the theorems hold

Abstract

We consider a symmetric block operator spectral problem with two spectral parameters. Under some reasonable restrictions, we state localisation theorems for the pair-eigenvalues and discuss relations to a class of non-self-adjoint spectral problems.