Revisiting Ulam stability for boundary value problems

doi:10.1016/j.nonrwa.2026.104618

Revisiting Ulam stability for boundary value problems

2026-02-01

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Agnieszka B. Malinowska

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Ewa Girejko

DOI：10.1016/j.nonrwa.2026.104618

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Abstract

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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.

Keywords:

Differential equation

Dynamic equation

Time scale

Boundary value problem

Ulam stability

Modified Ulam integral-stability

Modified Ulam differential-stability

Modified Ulam dynamic-stability

Revisiting Ulam stability for boundary value problems

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