时间测度链上二阶动力方程的振动性定理(英文)  

Oscillation theorems of second-order dynamic equation on time scales

作　　者：杨甲山[1] 刘兴元[1] 

机构地区：[1]邵阳学院理学与信息科学系,湖南邵阳422004

出　　处：《安徽大学学报（自然科学版）》2013年第1期8-12,共5页Journal of Anhui University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Hunan Province(12JJ6006);the Hunan Province Science and Technology Project(2012FJ3107);the National Natural Science Foundation of China(11071222)

摘　　要：研究时间测度链上的一类二阶非线性中立型时滞动力方程的振动性.首先,通过引入广义的Riccati变换,并借助时间测度链上的有关理论,得到了该类方程振动的充分条件;其次,利用Banach空间的不动点定理和一些分析技巧,得到了该类方程存在有界的最终正解的判别准则.所得结果是新的,并且推广和统一了现有文献中的一些相应的已知结果.In the paper,the oscillation for a class of second-order nonlinear neutral delay dynamic equation on time scales was discussed.First,the sufficient condition for oscillation of the equation was proposed by introducing the generalized Riccati transformation and the time scales theory.Second,a non-oscillation criterion that the equation has bounded eventually positive solutions was obtained by using the fixed point theorem in Banach space and some analysis techniques.These results are new and they unify and generalize some corresponding known results in this field.

关 键 词：时间测度链 动力方程 最终正解 RICCATI变换 振动性 

分 类 号：O175.7[理学—数学]