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Open Access Research Article

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

Hamza Menken

Author Affiliations

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

Boundary Value Problems 2010, 2010:720235  doi:10.1155/2010/720235

Published: 28 November 2010

Abstract

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.