二阶非线性中立型微分方程的振动性  

ON OSCILLATION OF SECOND ORDER NONLINEAR DELAY NEUTRAL DIFFERENTIAL EQUATIONS

作　　者：杨启贵[1] 朱思铭[2] 

机构地区：[1]清华大学数学科学系,北京100084 [2]中山大学数学系,广州510275

出　　处：《系统科学与数学》2003年第4期482-490,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11071097);广西自然科学基金(桂科基0236012)资助课题

摘　　要：利用广义Riccati变换和权函数积分平均技巧,建立了非线性时滞中立型方程:[r(t)(x(t)-p(t)x(t-τ))']'+q(t)f(x(t-δ))h(x'(t))=0的振动准则,其中τ和δ是非负常数,a,p,q∈C([to,∞),R),f和h∈C(R,R).这些结果补充了大量存在性结论和处理以前结果不能解决的问题.特别地,以实例说明本文结果是实质性推广.By using generalized Riccati transformation and weight function technique, new oscillation criteria are established in this paper for a second order nonlinear neutral delay differential equation [r(t)(x(t) - p(t)x(t - r))']' + q(t)f(x(t -δ))h(x'(t)) = 0 where T and δ are nonnegative constants, a, p, q ∈ C([to,∞),R), f, h ∈ C(R,R). These results complement a number of existing results and handle the case which are not covered by the known criteria. In particular, several examples that dwell upon the sharp conditions of our result are also included.

关 键 词：微分方程 振动性 RICCATI变换 权函数 积分 

分 类 号：O175.2[理学—数学]