We study hybrid dynamic systems on time scales. Using Lyapunov-like functions, we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales.
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By means of Riccati transformation technique, we establish some new oscillation criteria for third-order nonlinear delay dynamic equations $((x^{ΔΔ}(t))^γ)^Δ + p(t)x^γ(τ(t)) = 0$ on a time scale 𝕋; here γ > 0 is a quotient of odd positive integers and p a real-valued positive rd-continuous function defined on 𝕋. Our results not only extend and improve the results of T. S. Hassan [Math. Comput. Modelling 49 (2009)] but also unify the results on oscillation of third-order delay differential equations and third-order delay difference equations.
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