时间测度链上具正负系数的二阶阻尼动力方程的振动准则  

Oscillation Criteria for Second-Order Dynamic Equations with Positive and Negative Coefficients and Damping on Time Scales

作　　者：杨甲山[1] 

机构地区：[1]梧州学院数理系,广西梧州543002

出　　处：《数学物理学报（A辑）》2014年第2期393-408,共16页Acta Mathematica Scientia

基　　金：湖南省自然科学基金项目(12JJ6006);湖南省科技厅基金项目(2012FJ3107);广西教育厅科研项目(2013YB223);国家自然科学基金项目(11071222)资助

摘　　要：研究了时间测度链上一类具正负系数和阻尼项及非线性中立项的二阶变时滞非线性动力方程的振荡性.利用时间测度链上的有关理论及广义Riccati变换,结合大量不等式技巧,建立了该方程若干新的振动准则,这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了二阶非线性时滞阻尼微分方程和二阶非线性时滞阻尼差分方程的振动性质.The oscillation for certain second-order nonlinear variable delay dynamic equations with positive and negative coefficients and damping and nonlinear neutral on time scales is discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of second-order nonlinear delay differential equations with damping and second-order nonlinear delay difference equations with damping.

关 键 词：振动性 动力方程 时间测度链 正负系数 阻尼项 非线性中立项 

分 类 号：O175.7[理学—数学]