Oscillation analysis of second-order quasilinear damped dynamic equations on time scales
LI Jimeng1, YANG Jiashan2
1.School of Science, Shaoyang University, Shaoyang 422004, Hunan Province, China 2.School of Data Science and Software Engineering, Wuzhou University,Wuzhou 543002,Guangxi Zhuang Autonomous Region, China
Abstract：We investigate the oscillation of second-order quasilinear delay damped dynamic equation [a(t)|xΔ(t)|λ-1xΔ(t)]Δ+b(t)|xΔ(t)|λ-1xΔ(t)+p(t)|x(δ(t))|λ-1x(δ(t))=0, where t0 ∈ T and T is an arbitrary time scale, and the equation is in a noncanonical form, i.e., $\int^{∞}_{t_0}$[a-1(s)e-b/a(s,t0)]1/λ Δs < ∞. By using the generalized Riccati transformation, and incorporating with the time scales theory and the inequality technique, we establish some new sufficient conditions for the oscillation of the equation, these results deal with some cases not covered by existing results in the literature.
李继猛, 杨甲山. 时间尺度上二阶拟线性阻尼动力方程的振动性分析[J]. 浙江大学学报（理学版）, 2020, 47(1): 72-76.
LI Jimeng, YANG Jiashan. Oscillation analysis of second-order quasilinear damped dynamic equations on time scales. Journal of ZheJIang University(Science Edition), 2020, 47(1): 72-76.
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2020, Vol. 47 
