International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 92134, 26 pages

Maximal regular boundary value problems in Banach-valued function spaces and applications

Veli B. Shakhmurov

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

Received 27 December 2004; Accepted 30 September 2005

Copyright © 2006 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 differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valued Lp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.