B-essential spectra of 2 × 2 block operator matrix pencils

Abstract

The paper is devoted to the study of the relative B-essential spectra of 2 × 2 {2\times 2} unbounded operator matrix pencils defined with nondiagonal domain. The main tool used to prove the results is the Frobenuis–Schur factorization associated with this kind of operator matrix which has proven very useful in dealing with stability analysis in the theory of B-Fredholm operators pencils. Therefore, the theoretical results are tested in pencil transport integro-differential equation with specific boundary conditions.