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...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.展开更多
The integral inequality was an importantmethod in stability theory of nonlinear differentalsysfems. This paper presented a new integral inequalitywhose variable differential modules were greater than 1.The new integra...The integral inequality was an importantmethod in stability theory of nonlinear differentalsysfems. This paper presented a new integral inequalitywhose variable differential modules were greater than 1.The new integral inequality, the classical formula ofvariation of constants and Jensen inelquality wereeffective in dealing with the stability of a kind ofnonlinear neutral differential system with variationdelays. The several sufficient conditions of the stabilityproperties of nonlinear differential system with neutraldelays were established. The obtained results developedsome results which had been previously published.展开更多
文摘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.
文摘The integral inequality was an importantmethod in stability theory of nonlinear differentalsysfems. This paper presented a new integral inequalitywhose variable differential modules were greater than 1.The new integral inequality, the classical formula ofvariation of constants and Jensen inelquality wereeffective in dealing with the stability of a kind ofnonlinear neutral differential system with variationdelays. The several sufficient conditions of the stabilityproperties of nonlinear differential system with neutraldelays were established. The obtained results developedsome results which had been previously published.
