Glasnik Matematicki, Vol. 60, No. 1 (2025), 167-182. \( \)

DATKO TYPE CHARACTERIZATIONS FOR UNIFORM DICHOTOMY IN MEAN WITH GROWTH RATES FOR REVERSIBLE STOCHASTIC SKEW-EVOLUTION SEMIFLOWS IN BANACH SPACES

Tímea Melinda Személy Fülöp

Department of Mathematics, West University of Timişoara, Timişoara, România
e-mail:timea.moraru@e-uvt.ro

Abstract.   The main aim of this paper is to give characterizations of Datko type for the uniform dichotomy in mean with growth rates concept for reversible stochastic skew-evolution semiflows in Banach spaces. As particular cases, we obtain integral characterizations for uniform exponential dichotomy in mean. The obtained results are generalizations of well-known theorems about uniform \(h\)-dichotomy of variational systems in deterministic case.

2020 Mathematics Subject Classification.   93D20, 37L55, 34D05

Key words and phrases.   Growth rate, reversible stochastic skew-evolution semiflows, uniform \( h \)-dichotomy in mean

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https://doi.org/10.3336/gm.60.1.10

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