具超线性中立项时滞微分方程解的振动性  

Oscillation of Solutions to Delay Differential Equations with a Superlinear Neutral Term

作　　者：傅建辉[1] 冯滔[1] 

机构地区：[1]湖南城市学院数学系,湖南益阳413000

出　　处：《湖南文理学院学报（自然科学版）》2006年第1期7-9,共3页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省自然科学基金资助项目(04JJY3001)

摘　　要：在α>1且0<β<α情形下,研究了具超线性中立项时滞微分方程[x(t)?pxα(t?τ)]′+q(t)xβ(t?σ)=0,t≥t0,解的振动性.利用一些新的技巧,获得了保证上述方程所有解振动的几乎“sharp”振动准则和至少存在一个非振动解的非振动准则,所得结果补充和扩展了已有文献.The oscillatory behavior of solutions to the delay differential equations with super-linear neutral term [x（t）-px^α（t-τ）＇＋q（t）x^β（t-σ）]=0,t≥t0 is studied in the case when α〉1 and 0〈β〈α. By using some new technique, an almost ＂sharp＂ oscillatory criterion is obtaind which guarntees all solutions to the above equation oscillate and a non-oscillatory criterion that there exists at least a non-oscillatory solution. These results fill a gap in the literature.

关 键 词：中立型时滞微分方程 超线性中立项 振动性 

分 类 号：O175.10[理学—数学]