Datko type characterizations for exponential instability in average of cocycles

Topological dynamics of nonautonomous systems (37B55) Nonautonomous smooth dynamical systems (37C60) Stability theory for random and stochastic dynamical systems (37H30)

Cites Work

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A version of a theorem of R. Datko for stability in average
An extension of a theorem of E. A. Barbashin to the dichotomy of abstract evolution operators
A version of a theorem of R.\,Datko for nonuniform exponential contractions
Barbashin-type conditions for exponential stability of linear cocycles
Continuous and discrete characterizations for the uniform exponential stability of linear skew-evolution semiflows
On weak exponential stability of evolution operators in Banach spaces
The Lyapunov operator equation for the exponential dichotomy of one-parameter semigroups
Strong nonuniform behaviour: a Datko type characterization
New conditions for (non)uniform behaviour of linear cocycles over flows
Exponential instability of linear skew-product semiflows in terms of Banach function spaces
Barbashin type characterizations for the uniform polynomial stability and instability of evolution families
Admissible Banach function spaces and nonuniform stabilities
Polynomial stability and polynomial instability for skew-evolution semiflows
Integral conditions for nonuniform \(\mu\)-dichotomy on the half-line
Stability of nonautonomous differential equations
An extension of a theorem of R. Datko to the case of (non)uniform exponential stability of linear skew-product semiflows
Extending a theorem of A. M. Liapunov to Hilbert space
Uniform exponential dichotomy of stochastic cocycles
On the polynomial stability of evolution families
On two theorems regarding exponential stability
Lyapunov theorems for the asymptotic behavior of evolution families on the half-line
Exponential dichotomies in average for flows and admissibility
Exponential stability and exponential instability for linear skew-product flows
Datko type characterizations for nonuniform polynomial dichotomy
On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces
Datko-Pazy conditions for nonuniform exponential stability
Admissibility for exponential dichotomies in average
Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space
On the Applicability of Lyapunov’s Theorem in Hilbert Space
Remarks on the Control of Discrete-Time Distributed Parameter Systems

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