Abstract
The main goal of this paper is to apply Ulam stability theory to boundary value problems for dynamic equations, while addressing several common misconceptions found in the existing literature. We identify the key issues that arise when applying Ulam stability to such problems and propose three distinct approaches to overcome them. To enhance clarity and accessibility, we begin with nonlinear ordinary differential equations and subsequently extend the analysis to nonlinear dynamic equations on time scales. Since a time scale is defined as any nonempty closed subset of the real numbers, our results are applicable to dynamic equations on continuous, discrete, or hybrid time domains.
Recommended Citation
M. Bohner et al., "Revisiting Ulam Stability for Boundary Value Problems," Nonlinear Analysis Real World Applications, vol. 92, article no. 104618, Elsevier, Dec 2026.
The definitive version is available at https://doi.org/10.1016/j.nonrwa.2026.104618
Department(s)
Mathematics and Statistics
Publication Status
Full Text Access
Keywords and Phrases
Boundary value problem; Differential equation; Dynamic equation; Modified Ulam differential-stability; Modified Ulam dynamic-stability; Modified Ulam integral-stability; Time scale; Ulam stability
International Standard Serial Number (ISSN)
1468-1218
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Publication Date
01 Dec 2026
Comments
Ministerstwo Edukacji i Nauki, Grant KP-06-N62/1