On the solvability and the dimension of the solution set of abstract linear boundary value problems and applications to ODE'S

Document Type

Article

Publication Date

6-1-2024

Abstract

A solvability theory for linear abstract boundary value problems, that is of linear operator equations subject to an additional (“boundary”) condition given by a linear operator, is developed using a new approach based on normal solvability of the induced map or a pseudoinverse of the boundary map when restricted to the null space of the homogeneous problem. Uniqueness and dimension of their solution sets is also established. Applications to BVP's for finite-dimensional as well as infinite-dimensional systems of ordinary differential equations defined on the half line or the whole line are given. Systems having exponential dichotomy, or satisfying Riccati type inequalities are studied, as well as systems with asymptotically hyperbolic linear part and systems between pairs of admissible Banach spaces.

Identifier

85180298847 (Scopus)

Publication Title

Journal of Mathematical Analysis and Applications

External Full Text Location

https://doi.org/10.1016/j.jmaa.2023.128029

e-ISSN

10960813

ISSN

0022247X

Issue

1

Volume

534

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