A characterization of exponential stability for periodic evolution families in terms of lower semicontinuous functionals.
A spectral mapping theorem for evolution semigroups on asymptotically almost periodic functions defined on the half line.
A new theorem on exponential stability of periodic evolution families on Banach spaces.
Exponential stability of linear and almost periodic systems on Banach spaces.
New characterizations of asymptotic stability for evolution families on Banach spaces.
The Hardy-Landau-Littlewood inequalities with less smoothness.
A theorem of Rolewicz's type for measurable evolution families in Banach spaces.
Local attractivity in nonautonomous semilinear evolution equations
We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...
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