Glasnik Matematicki, Vol. 59, No. 1 (2024), 107-123. \( \)

ON UNIFORM INSTABILITY IN MEAN OF STOCHASTIC SKEW-EVOLUTION SEMIFLOWS

Tian Yue

School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, 442002 Shiyan, China
e-mail:yuet@huat.edu.cn

Abstract.   In this paper we study three concepts of uniform instability in mean for stochastic skew-evolution semiflows: uniform exponential instability in mean, uniform polynomial instability in mean and uniform \(h\)-instability in mean. These concepts are natural generalizations from the deterministic case. Connections between these concepts are presented. Additionally, some expansion properties, logarithmic criteria and majorization criteria of these concepts are given, respectively.

2020 Mathematics Subject Classification.   34D05, 37L55

Key words and phrases.   Stochastic skew-evolution semiflows, uniform exponential instability in mean, uniform polynomial instability in mean, uniform \(h\)-instability in mean

https://doi.org/10.3336/gm.59.1.05

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