摘要
研究一阶非线性中立型时滞微分方程[x(t)-pxα(t-π)]′+f(t,x(t-σ))=0,t>t0的解的振动性,在p,τ∈(0,∞),σ∈[0,∞],α≠1,f(t,x)为定义在[t0,+∞]×R上的连续函数的情形下获得了上述方程每个有界解振动的一个充分条件和一个必要条件,拓广文[5]的主要结果。
In this paper, oscillation of nonlinear neutral delay differential equation [ x (t) - px^α ( t - π) ]' +f(t,x(t-σ) ) =0,t 〉 to is considered. A sufficient condition and a necessary condition are obtained which guarantee every bounded solutions of the above equation oscillates in the case when p, T ∈(0, ∞ ), σ ∈ [ 0, ∞ ], α ≠ 1 and f( t ,x) is continuous function of [ t0, + ∞ ] × R. The results generalize main result of literature [ 5 ].
出处
《长春理工大学学报(自然科学版)》
2006年第2期116-117,90,共3页
Journal of Changchun University of Science and Technology(Natural Science Edition)
关键词
非线性
中立型
时滞微分方程
振动性
nonlinear
neutral type
delay differential equation
oscillation