Existence and stability of solutions of certain neutral-type differential equations = Existence et stabilité de solutions de certaines équations différentielles de type neutre
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Date
2026
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Université Badji Mokhtar Annaba
Abstract
The objective of this thesis is to study the existence and stability of periodic solutions for certa in neutral differential equations and systems with time delays and variable coefficients. UsingKrasnoselskii’s fixed point theorem, we present a set of sufficient conditions that guarantee the existence of periodic solutions. This involves transforming the system into an equivalent integral form before applying fundamental matrix solutions in parallel with Floquet theory. In addition, we analyze the asymptotic stability of these solutions, leading to new conditions that can ensure stability. The practical significance of our theoretical results is supported by numerical examples, which verify the validity of the proposed approach and highlight its applicability in various fields such as electrical circuits, power transmission and signal propagation problems, control systems, and biological modeling. This study extends previous work by providing a detailed framework tailored to the study of neutral differential systems with time delays.
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Keywords
neutral differential equations and systems; time delays; fixed point; floquet
theory; fundamental matrix solutions; krasnoselskii; periodic solutions; asymptotic stability