On uniform exponential trichotomy of evolution operators in Banach spaces (Q930455)

The known results of [\textit{R. Datko}, ``Uniform asymptotic stability of evolutionary processes in Banach spaces'', SIAM J. Math. Anal. 3, 428--445 (1972; Zbl 0241.34071)] and more later ones on the theory of stability of linear evolution operators in Banach spaces are extended into two directions: {\parindent=6,5mm \begin{itemize}\item[(1)] the linearity of evolution operators is not assumed; \item[(2)] necessary and sufficient conditions are obtained for uniform exponential trichotomy of nonlinear evolution operators. \end{itemize}}