侯成敏,何延生.一类二阶非线性泛函微分方程的振动性[J].数学研究及应用,2000,20(4):555~561 |
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 |
投稿时间:1997-09-11 修订日期:1999-06-21 |
DOI:10.3770/j.issn:1000-341X.2000.04.015 |
中文关键词: 振动 积分平均 非线性. |
英文关键词:oscillation integral average nonlinear. |
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摘要点击次数: 2022 |
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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. |
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