Nonlinear differential equations with asymptotically stable solutions

We establish conditions of asymptotic stability of all solutions of the equation , t≥0in a Banach space E in the case where σ(A(x)⊂{λ:Reλ<0}∀x∈E. We give an example of an equation with unstable solutions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 264–273, February, 1998.