Continuous parameter dependence for solutions of one-dimensional boundary value problems
Tanya Kodliuk, Vladimir Mikhailets, Nadya Reva
TL;DR
This paper studies how solutions to one-dimensional boundary value problems depend continuously on parameters, extending existing theorems and providing conditions for Green matrix convergence.
Contribution
It generalizes Kiguradze's theorem on boundary value problem correctness and establishes conditions for Green matrix convergence.
Findings
Extended Kiguradze's theorem on correctness.
Provided sufficient conditions for Green matrix convergence.
Ensured uniform convergence of Green matrices.
Abstract
We investigate continuous parameter dependence for solutions of general boundary value problems for ordinary linear differential systems. The generalization of Kiguradze's theorem (1987) on correctness of such problems was obtained. Also sufficient conditions for the Green matrices of such problems to converge uniformly to the Green matrix of the limiting problem were found.
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Taxonomy
TopicsMaterial Science and Thermodynamics · Differential Equations and Numerical Methods · Mathematical Control Systems and Analysis