Fredholm Boundary Value Problems for Perturbed Systems of Dynamic Equations on Time Scales

Abstract

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore-Penrose pseudo-inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Boundary value problems; Difference equations; Time measurement; Vector spaces; Dynamic equations; Existence of Solutions; Fredholm; Linear boundary value problem; Linearly independents; Moore Penrose pseudo inverse; Perturbed systems; Time-scales; Inverse problems; Dynamic equations on time scales; Fredholm boundary value problems

International Standard Serial Number (ISSN)

0170-4214; 1099-1476

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 John Wiley & Sons, All rights reserved.

Publication Date

01 Nov 2015

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