Linear and Nonlinear Nonlocal Boundary Value Problems for Differential-operator Equations
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.
R. P. Agarwal et al., "Linear and Nonlinear Nonlocal Boundary Value Problems for Differential-operator Equations," Applicable Analysis, Taylor & Francis, Jan 2006.
The definitive version is available at https://doi.org/10.1080/00036810500533153
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
Article - Journal
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