多滞量非自治中立型泛函微分方程的3/2-渐近稳定性

On the 3/2-Asymptotic Stability of Nonautonomous Neutral Differential Equations with Delays

考虑多滞量非自治中立型泛函微分方程ddt x(t) - ∑mi=1fi(t,x(t-τi) ) +∑nj=1gj(t,x(t-δj) ) =0 ,t t0 ,其中τi,δj∈ (0 ,∞ ) ,fi,gj∈ C([t0 ,∞ )× R,R) ,i=1 ,2 ,… ,m,j=1 ,2 ,… ,n,且当 t t0 ,x∈R时 ,x .gj(t,x) 0 ,j=1 ,2 ,… ,n,获得了该方程零解一致稳定和渐近稳定的充分条件 ,推广并改进了现有文献中的相关结论 .

Consider the nonautonomous neutral differential equa tionddtx(t)-∑mi=1f i(t, x(t- τ i))+∑nj=1g j(t,x(t-δ j))=0, tt 0,where τ i, δ j∈(0,∞),f i, g j∈C(On the 3/2-Asymptotic Stability of NonautonomousNeutral Differential Equations with Delays$$$$ Wu Zhaohua1 Luo Zhiguo1 Wang Zhiming2(1. College of Mathematics and Computer Science, Hunan Normal Univers ity, Changsha Hunan 4100812. Department of Information Science, Hunan Agriculture University, Changsha Hun an 410128) Abstract Consider the nonautonomous neutral differential equa tionddtx(t)-∑mi=1f i(t, x(t- τ i))+∑nj=1g j(t,x(t-δ j))=0, tt 0,where τ i, δ j∈(0,∞),f i, g j∈C([t 0,∞)×R, R), i=1,2,..., m, j=1,2,...,n, and x·g j(t, x)0 for tt 0,x∈R, j=1,2,...,n. We obtain the sufficient conditions for the zero solution of this equation to b e uniformly stable as well as asymptotic stable. Some known results in the liter ature are extended and improved.