具阻尼项的一类二阶非线性动态方程的振动准则（英文）  

Oscillation Criteria for Certain Second-order Nonlinear Dynamic Equations with Damping

作　　者：杨甲山[1] 苏芳[1] 

机构地区：[1]梧州学院数理系,广西梧州543002

出　　处：《应用数学》2014年第2期392-404,共13页Mathematica Applicata

基　　金：the Natural Science Foundation of Hunan Province(12JJ6006);the Hunan Province Science and Technology Project(2012FJ3107);the National Natural Science Foundation ofChina(11071222);the Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)

摘　　要：本文研究时间测度链上的一类具阻尼项和非线性中立项的二阶非线性变时滞泛函动态方程[A(t)(yΔ(t))]Δ+b(t)(yΔ(t))+P(t)F((x(δ(t))))-Q(t)f((x(γ(t))))=0,的振动性质,式中T为任一时间测度链且supT=+∞,y(t)=x(t)+B(t)g(x(τ(t))),(u)=|u|λ-1 u,λ>0.利用时间测度链上的理论和广义Riccati变换及不等式技巧,建立该方程的若干新的振动准则,这些准则不仅补充和改进了现有文献中的相关结论,而且改进了具有阻尼项和中立项的二阶动态方程的一些已知振动理论,更进一步,本文的主要结果还改良了相应的二阶时滞微分方程和差分方程的振动准则.并给出一些例子来说明研究结果的重要性.This paper is concerned with the oscillatory behavior of a certain class of second-order nonlinear variable delay functional dynamic equations with damping and nonlinear neutral, [A（t）Ф（y△（t））]△＋b（t）Ф（y△（t））＋P（t）F（Ф（x（δ（t））））-Q（t）f（Ф（x（γ（t））））=0, on a time scale T with supT==＋∞,where y（t）=x（f）十B（t）g（x（τ（t）））,Ф（u）=｜u｜λ-1u,λ〉0. By using the time scales theory and the generalized Riceati transformation and the inequality technique, some new oscillation criteria for the equations are established, results are presented that not only complement and improve those related results in the literature, but also improve some known results for a second-order delay dynamic equation with damping and a neutral term. Further, the main results improve some related results for second-order neutral differential equations and difference equations. Some examples are given to illustrate the importance of our results.

关 键 词：振动性 动力方程 时间测度链 阻尼项 非线性中立项 

分 类 号：O175.7[理学—数学]