Fredholm Boundary Value Problems for Perturbed Systems of Dynamic Equations on Time Scales
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.
R. P. Agarwal et al., "Fredholm Boundary Value Problems for Perturbed Systems of Dynamic Equations on Time Scales," Mathematical Methods in the Applied Sciences, vol. 38, no. 17, pp. 4178-4186, John Wiley & Sons, Nov 2015.
The definitive version is available at https://doi.org/10.1002/mma.3356
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)
Article - Journal
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01 Nov 2015