On spectral properties of a fourth-order boundary value problem

Abstract

In this work, we study a fourth-order boundary value problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. We discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions.

Keywords

• Asymptotics of eigenvalues and eigenfunctions
• Transmission conditions
• Fourth-order differential operator
• Spectrum