On spectral properties of a fourth-order boundary value problem

In this work, we study a fourthorder 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. (C) 2012 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved