具有分布偏差变元的二阶中立型时滞微分方程的振动性

Oscillation of Second-Order Neutral Delay Differential Equations with Distributed Deviating Argument

考虑如下具有分布偏差变元的二阶中立型时滞微分方程:(r(t)ψ(x(t))Z′(t))′+integral (p(t,ξ)f[x(g(t,ξ))]dσ(ξ)) from n=a to b=0(t≥t0)的振动性,其中Z(t)=x(t)+q(t)x(t-τ),τ≥0.利用广义的Riccati技巧和积分均值不等式,并借助于一类新函数Φ(t,s,l)和类函数F,放宽了对函数f的限制,即当f不满足下述条件:存在一个正数M,使得︱f(±uv)︱≥Mf(u)f(v),uv>0时,建立了具有分布偏差变元的二阶中立型时滞微分方程新的振动准则,数值实例验证了所得结果的正确性.

The oscillation of second-order neutral delay differential equations with distributed deviating argument：（r（t）ψ（x（t））Z′（t））′＋integral （p（t,ξ）f[x（g（t,ξ））]dσ（ξ）） from n=a to b=0（t≥t0）,where Z（t） = x（t） ＋ q（t） x（t-τ）,τ≥0 was investigated via a generalized Riccati technique and the integral averaging inequality,a class of new functions Φ（t,s,l） and the function class F,we relaxed the restriction on function f,namely,when f does not satisfy the following conditions：there exists M 0,such that ︱f（± uv）︱≥Mf（u） f（v）,uv 0,and hence established some new oscillation criteria for second-order neutral equations with distributed deviating argument.An example was given to illustrate the results.