Abstract and Applied Analysis
Volume 2007 (2007), Article ID 51410, 27 pages
Research Article

Degenerate Differential Operators with Parameters

Veli B. Shakhmurov

Department of Electrical-Electronics Engineering, Faculty of Engineering, Istanbul University, Avcilar 34320, Istanbul, Turkey

Received 29 September 2006; Accepted 28 February 2007

Academic Editor: Pavel E. Sobolevskii

Copyright © 2007 Veli B. Shakhmurov. 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.


The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valued Lp spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.