二阶非线性中立型动力方程的振动定理  

Oscillation theorems for second-order nonlinear neutral dynamic equations

作　　者：韩忠月[1] 

机构地区：[1]德州学院数学科学学院,山东德州253023

出　　处：《华中师范大学学报（自然科学版）》2014年第5期627-631,共5页Journal of Central China Normal University：Natural Sciences

摘　　要：借助时间尺度的有关理论,利用广义Riccati变换和加权平均不等式,讨论时标上二阶非线性中立型动力方程(r(t)[(x(t)+a(t)x(τ(t)))Δ]α)Δ+∫dcF(t,ξ,x(δ(t,ξ)))Δξ+∑ni=1∫dcFi(t,ξ,x(δ(t,ξ)))Δξ=0,t∈Τ的振动性,其中,α是奇整数之商.获得了动力方程振动的充分条件.该文结论推广和改进了已有文献的有关结果,并给出了应用实例.By the theory of time scales,generalized Riccati transformation and weighted mean value inequality,we establish oscillation criteria for the following second-order nonlinear neutral dynamic equation on time scales,（r（t）[（x（t）＋a（t）x（τ（t）））^△]α）^△＋∫c^dF（t,ξ,x（δ（t,ξ）））△ξ＋∑i=i^n=1∫c^dFi（t,ξ,x（δ（t,ξ）））△ξ=0,t∈T,where α is the ratio of two odd positive integers.New sufficient conditions are obtained for oscillations of this equation.Some relevant results in the existing papers are improved and generalized in this paper.Finally,several examples are given to illustrate the applications of the obtained results.

关 键 词：二阶非线性中立型动力方程 振动定理 时标 

分 类 号：O175[理学—数学]