I recently had a chance to ask a professor this question and he mentioned that this is true for ordinary differential equations (but not for delay differential equation). He did not remember the reference, I could not find a reference for this, so can anyone please point me to the right source?
2026-03-26 01:00:28.1774486828
Does globally stability implies existence of Lyapunov function?
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You will find what you need in this paper and the references of Karafyllis:
Converse Lyapunov–Krasovskii theorems for systems described by neutral functional differential equations in Hale's form
Pierdomenico Pepe & Iasson Karafyllis