一类二阶非线性泛函微分方程的振动性

Oscillations for a Class of Second Order Nonlinear Differential Equations

中文关键词:  振动  积分平均  非线性.

英文关键词:oscillation  integral average  nonlinear.

中文摘要:

      本文讨论二阶非线性泛函微分方程(a(t)y′(t))′+p(t)y′(t-τ(t))-q(t)f(y(t))=0,t≥t₀，(1)(a(t)y′(t))′-p(t)y′(t+τ(t))-q(t)f(y(t))=0,t≥t₀，(2)获得了方程(1)和(2)振动的充分性判据，推广和改进了已知的一些结果.

英文摘要:

      In this paper, we disscuss a class of second order nonlinear differential equations (a(t)y′(t))′+p(t)y′(t-τ(t))-q(t)f(y(t))=0,　t≥t₀(1) and (a(t)y′(t))′-p(t)y′(t+τ(t))-q(t)f(y(t))=0,　t≥t₀(2) where, a(t),p(t),q(t),τ(t)∈C ［(t₀，∞),(0,∞)］,f(u)∈C(R,R)， sufficient conditions are obtained for all solutions of the equations to be oscillatory.