ACTA issues

A version of a theorem of A.~M. Lyapunov for the stability and instability of evolution families in Banach spaces

Cristina Pra?a

Acta Sci. Math. (Szeged) 80:3-4(2014), 539-552

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.)