Open Access

Maximal regular boundary value problems in Banach-valued weighted space

Boundary Value Problems20052005:720289

DOI: 10.1155/BVP.2005.9

Received: 10 July 2004

Published: 2 February 2005


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 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.

Authors’ Affiliations

Department of Mathematical Sciences, Florida Institute of Technology
Department of Mathematics, University of Missouri-Rolla
Department of Electrical-Electronics Engineering, Faculty of Engineering, Istanbul University


© Agarwal et al. 2005