Boundary Value Problems
Volume 2010 (2010), Article ID 720235, 21 pages
Research Article

Accurate Asymptotic Formulas for Eigenvalues and Eigenfunctions of a Boundary-Value Problem of Fourth Order

Mathematics Department, Science and Arts Faculty, Mersin University, 33343 Mersin, Turkey

Received 7 July 2010; Accepted 9 November 2010

Academic Editor: I. T. Kiguradze

Copyright © 2010 Hamza Menken. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the present paper, we consider a nonself-adjoint fourth-order differential operator with the periodic boundary conditions. We compute new accurate asymptotic expression of the fundamental solutions of the given equation. Then, we obtain new accurate asymptotic formulas for eigenvalues and eigenfunctions.