Linear and Nonlinear Nonlocal Boundary Value Problems for Differential-operator Equations

Abstract

This study focuses on nonlocal boundary value problems (BVPs) for linear and nonlinear elliptic differential-operator equations (DOEs) that are defined in Banach-valued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal Lp-regularity and Fredholmness of linear BVPs, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness and maximal smoothness of solutions of nonlocal BVPs for nonlinear DOEs are shown. These results are applied to nonlocal BVPs for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Banach-valued function spaces; Boundary value problems; Differential-operator equations; Interpolation of Banach space; Maximal Lp-regularity; Operator-valued multipliers

International Standard Serial Number (ISSN)

0003-6811

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Taylor & Francis, All rights reserved.

Publication Date

01 Jan 2006

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