非线性中立型时滞方程解的全局渐近稳定性和振动性

Global Asymptotic Stability and Oscillation of Solutions to a Nonlinear Neutral Delay Equation

本文研究非线性中立型时滞微分方程N( t) =N( t) [a( t) -b( t) N ( t-τ) -c( t) N( t-σ) -d( t) N ( t) ],t≥ t0 ,( E)其中τ,σ∈ [0 ,∞ ) ,a( t) ,b( t) ,d( t)∈ C1( [t0 ,∞ ) ,R+) ,c( t)∈ C( [t0 ,∞ ) ,k) ,得到方程 ( E)的正解关于正常数平衡点全局渐近稳定和振动的充分条件 .本文所用方法与其他文献不同 ,所得结果发展了一些文献的结果 ,其中定理 ( 2 .3)回答了由 Y.Kuang and A.Feldstein所提出的一个公开问题 .

This paper studies the nonlinear neutral delay equation(t)=N(t)\[a(t)-b(t)N(t-τ)-c(t)[AKN·](t-σ)-d(t)N(t)\], , for all t≥t\-0,(E)where τ,σ∈\[0,∞), a(t),b(t),d(t)∈C\+1(\[t\-0,∞),R\++),c(t)∈C(\[t\-0,∞),R).[WTBZ] Sufficient conditions are obtained for the boundedness of solutions and for global asymptotic stability and oscillation of positive constant equilibrium point of the positive solutions to the equation (E). The methods applied to the paper are different from other references. Results obtained in this paper extend those in \～\, and theorem (2 3) answers an open question proposed by Kuang Y and Feldstein A (\P.303).