Abstract and Applied Analysis
Volume 2009 (2009), Article ID 934905, 21 pages
doi:10.1155/2009/934905
Research Article

On the Differential Operators with Periodic Matrix Coefficients

O. A. Veliev

Department of Mathematics, Dogus University, Acıbadem, Kadiköy, Istanbul, Turkey

Received 26 March 2009; Revised 22 July 2009; Accepted 26 September 2009

Academic Editor: Ağacik Zafer

Copyright © 2009 O. A. Veliev. 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.

Abstract

We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then by using these asymptotic formulas, we find conditions on the coefficients for which the number of gaps in the spectrum of the self-adjoint differential operator with the periodic matrix coefficients is finite.