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Open Access Research Article

Maximal regular boundary value problems in Banach-valued weighted space

Ravi P Agarwal1*, Martin Bohner2 and Veli B Shakhmurov3

Author Affiliations

1 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA

2 Department of Mathematics, University of Missouri-Rolla, Rolla, MO 65409-0020, USA

3 Department of Electrical-Electronics Engineering, Faculty of Engineering, Istanbul University, Avcilar, Istanbul 34850, Turkey

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Boundary Value Problems 2005, 2005:720289  doi:10.1155/BVP.2005.9

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2005/1/720289

Received:10 July 2004
Published:2 February 2005

© 2005 Agarwal et al.

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.