Abstract
For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
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Arzarello, E., Bacciotti, A. On Stability and Boundedness for Lipschitzian Differential Inclusions: The Converse of Lyapunov's Theorems. Set-Valued Analysis 5, 377–390 (1997). https://doi.org/10.1023/A:1008603707291
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DOI: https://doi.org/10.1023/A:1008603707291