On the maximal asymptotics for linear differential equations in Banach spaces (Q536458)

The author considers the linear differential equation \[ dx/dt=Ax, \] where \(A\) is the generator of a \(C_0\)-semigroup in a Banach space. The work develops an approach proposed in 1982 by the author and Y. Ya. Shirman for the analysis of asymptotic stability of a linear differential equation in a Banach space. In particular, it is shown that the suggested method allows to prove the nonexistence of a fastest growing solution for a wide class of linear equations.