时间尺度上二阶拟线性阻尼动力方程的振动性分析

Oscillation analysis of second-order quasilinear damped dynamic equations on time scales

研究二阶拟线性时滞阻尼动力方程[a(t)|x^Δ(t)|^λ-1xΔ(t)]^Δ+b(t)|x^Δ(t)|^λ-1x^Δ(t)+p(t)|x(δ(t))|^λ-1x(δ(t))=0的振动性,其中t0∈T,而T为任意时间尺度,考虑方程是非正则情形,即∫∞[a-1(s)e-b/a(s,t0)]1/λ^Δs<∞。通过引入广义Riccati变换,借助时间尺度上的有关理论,并结合不等式技t0巧,建立了该方程振动的一些新的充分条件,推广、改进并丰富了现有文献中的结果。

We investigate the oscillation of second-order quasilinear delay damped dynamic equation[a(t)|x^Δ(t)|^λ-1 x^Δ(t)]^Δ+b(t)|x^Δ(t)|^λ-1 x^Δ(t)+p(t)|x(δ(t))|^λ-1 x(δ(t))=0,where t0∈T and T is an arbitrary time scale,and the equation is in a noncanonical form,i.e.,∫t0∞[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.