On the Riesz basis property of the root functions of a discontinuous boundary problem

Abstract

In this paper, we consider the nonself-adjoint discontinuous Sturm Liouville operator with periodic (antiperiodic) boundary condition and compatibility conditions. Asymptotic formulas of eigenvalues and eigenfunctions of the operator are obtained. Using these accurate asymptotic formulas for eigenvalues and eigenfunctions, we prove the basisness of the root functions of the boundary value problem.

Asymptotic Expressions of Fourth Order Sturm-Liouville Operator with Conjugate Conditions

“…Linear diferential operator order 𝑛 with strongly regular boundary conditions and conjugate conditions is firstly investigated by (Muravei, 1967). For second order boundary value problem with periodic (antiperiodic) and conjugate conditions are studied in several works (Cabri, 2019, Cabri and.…”