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Abstract. In the present paper we give some characterizations for the stability and instability of the evolution families by using the Lyapunov function, in Banach spaces. These results are a generalization of those obtained by N.U. Ahmed in [1] for the case of $C_0$-semigroups.
DOI: 10.14232/actasm-012-566-4
AMS Subject Classification
(1991): 34D05, 34D09, 47D06, 93D20
Keyword(s):
evolution family,
Lyapunov operator inequality,
exponential stability,
exponential instability
Received August 31, 2012, and in revised form April 25, 2014. (Registered under 66/2012.)
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