具有分布偏差变元的二阶中立型时滞微分方程的振动性

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)fx(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),uv0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.

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

The oscillation of second\|order neutral delay differential equations with distributed deviating argument, a class of new functions Φ(t,s,l) and the function cl
ass 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.