具有非正系数的一阶中立型滞后微分方程的振动性和渐近性质

Oscillatory and Asymptotic Properties of First Order Delay Neutral Differential Equations with Nonpositive Coefficients

中文摘要:

      本文对较文[1,2]中更为广泛的具有非正系数的一类线性方程d/(dt)[x(t)+p(t)x(t-τ)]-Q(t)x(t-σ(t))=0,t≥t₀及非线性方程d/(dt)[x(t)+p(t)x(t-τ(t))]-Q(t)f(x(t-σ(t)))=0,t≥t₀进行了讨论,其中Q(t)∈C([t₀,+∞).R₊),得到了保证上述方程的所有有界解振动及非振动解当t→+∞时趋于零或±∞的一些充分性准则.

英文摘要:

      In this paper, we deal with the osicllatory and asymptotic properties of the solutions for the neutral delay differential equations d/(dt)[x(t)+p(t)x(t-τ)]-Q(t)x(t-σ(t))=0,t≥t₀ and d/(dt)[x(t)+p(t)x(t-τ(t))]-Q(t)f(x(t-σ(t)))=0,t≥t₀,where p(t)∈C([t₀,+∞,R),Q(t)∈C([t₀,+∞),R₊),τ(t),σ(t)∈C([t₀,+∞),R₊), f∈C(R,R),f(u)u>0(u≠0). Some sufficient Conditions which keep all the boundedsolutions oscillating and all the solutions tending to zero or±∞(as t→+∞) are obtained.