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- W3021286040 abstract "Some phenomena in nature are characterized by the fact that their states are subject to sudden changes at certain moments and therefore can be described by impulsive system. In this chapter, we discuss impulsive dynamic equations on translation time scales. In Sect. 7.1, the Cauchy matrix and Liouville’s formula of linear homogeneous impulsive dynamic equations on time scales are derived and their almost periodicity is analyzed. In Sect. 7.2, on complete-closed time scales, we discuss a class of impulsive nonlinear dynamic equations through the almost periodic Cauchy matrix and equipotentially almost periodic sequences of their corresponding linear impulsive homogeneous dynamic equations, and some sufficient conditions on the existence and exponential stability of piecewise almost periodic solutions are obtained. In Sect. 7.3, as a generalization of piecewise almost periodic solutions, the dynamical behavior of weighted piecewise pseudo almost periodic solutions for impulsive dynamic equations is investigated on CCTS. In Sect. 7.4, we introduce the concept of e-equivalent impulsive functional dynamic equations (FDE) on ACCTS and propose the double-almost periodic impulsive FDE, and some sufficient conditions on the existence and uniqueness of double-almost periodic solutions are established. Finally, we investigate the existence and exponential stability of weighted piecewise pseudo double-almost periodic solutions for a class of e-equivalent impulsive evolution equations and several real applications are provided." @default.
- W3021286040 created "2020-05-13" @default.
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- W3021286040 date "2020-01-01" @default.
- W3021286040 modified "2023-09-30" @default.
- W3021286040 title "Impulsive Dynamic Equations on Translation Time Scales" @default.
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- W3021286040 doi "https://doi.org/10.1007/978-3-030-38644-3_7" @default.
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