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Nonuniform exponential unstability of evolution operators in Banach spaces. (English) Zbl 1008.34053
Summary: Here, the authors consider a nonuniform instability concept for evolution operators in Banach spaces. A relationship between this concept and the Perron condition is studied. Generalizations to the nonuniform case of some results of Nguyen Van Minh, F. Räbiger and R. Schnaubelt [Integral Equations Oper. Theory 32, No. 3, 332-353 (1998; Zbl 0977.34056)] are obtained. The theory presented is applicable for general time-varying linear equations in Banach spaces.

34G10 Linear differential equations in abstract spaces
34D20 Stability of solutions to ordinary differential equations