Dynamical Behavior of Second-order Quasilinear Delay Damped Dynamic Equations on Time Scales
LI Jimeng1, YANG Jiashan2
1. School of Science, Shaoyang University, Shaoyang 422004, China; 2. School of Data Science and Software Engineering, Wuzhou University, Wuzhou 543002, China
Abstract：The dynamical behavior of certain second-order quasilinear variable delay damped dynamic equations are investigated on a time scale T, where the equations are noncanonical form (i.e.,∫t0∞ [a-1(s)e-b/a(s, t0)] 1/λ Δs<∞). By using the generalized Riccati transformation, and in combination with the time scales theory and the classical inequality, some new oscillation criteria for the equation are established. The results fully reflect the influential actions of delay functions and damping terms in system oscillation. Finally, some examples are given to show that our results extend, improve and enrich those reported in the literature, and that they have good effectiveness and practicability.
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2020, Vol. 43 
