Boundary Value Problems
Volume 2005 (2005), Issue 1, Pages 9-42

Maximal regular boundary value problems in Banach-valued weighted space

Ravi P. Agarwal,1 Martin Bohner,2 and Veli B. Shakhmurov3

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Mathematics, University of Missouri-Rolla, Rolla 65409-0020, MO, USA
3Department of Electrical-Electronics Engineering, Faculty of Engineering, Istanbul University, Avcilar, Istanbul 34850, Turkey

Received 10 July 2004

Copyright © 2005 Ravi P. Agarwal et al. 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.


This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to obtain the algebraic conditions that guarantee the same properties.