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Matrix Lyapunov functions method for sets of dynamic equations on time scales. (English) Zbl 1517.34119

Stability theory of set diferential equations on time scales is studied. The definition of a regressive set valued map on a time scale (Definition 2.6) involves an addition operation between a scalar and an element of \(\mathbb{K}_c(\mathbb{R}^n)\), the function \(\Theta X(t)\) given in Definition 2.7 includes a quotient of two elements of \(\mathbb{K}_c(\mathbb{R}^n)\) and the the operation \(\oplus\) includes a ‘product’ of two elements of \(\mathbb{K}_c(\mathbb{R}^n)\). The meaning of these on a time scale where the graininess function \(\mu(t) \not\equiv 0\) is not clear. The formulation of the Hukuhara derivative and the results obtained in the paper depend on the above notions. An illustative example on a nonstandard timescale would have added some insight.

MSC:

34N05 Dynamic equations on time scales or measure chains
34A60 Ordinary differential inclusions
34D20 Stability of solutions to ordinary differential equations
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