Boundary Value Problems
Volume 2009 (2009), Article ID 710386, 20 pages
doi:10.1155/2009/710386
Research Article

On the Correct Solvability of the Boundary-Value Problem for One Class Operator-Differential Equations of the Fourth Order with Complex Characteristics

Araz R. Aliev1,2 and Aydin A. Gasymov1

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9 F. Agaev street, Baku, AZ1141, Azerbaijan
2Baku State University, 23 Z. Khalilov street, Baku, AZ1148, Azerbaijan

Received 19 February 2009; Revised 22 July 2009; Accepted 26 August 2009

Academic Editor: Ivan T. Kiguradze

Copyright © 2009 Araz R. Aliev and Aydin A. Gasymov. 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

Sufficient coefficient conditions for the correct and unique solvability of the boundary-value problem for one class of operator-differential equations of the fourth order with complex characteristics, which cover the equations arising in solving the problems of stability of plastic plates, are obtained in this paper. Exact values of the norms of operators of intermediate derivatives, which are involved in the perturbed part of the operator-differential equation under investigation, are found along with these in subspaces W24(R+;H) in relation to the norms of the operator generated by the main part of this equation. It is noted that this problem has its own mathematical interest.