高阶泛函微分方程的振动性质<sup>*</sup>

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高阶泛函微分方程的振动性质^*

基金项目: * 广东省高等学校基础研究课题

Departmant of Mathematics, Hanshan Teacher's College, Chaozhou, Guangdong 521041, P. R. China

摘要: 本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程的振动性质.文中指出.在一定条件下,方程的非振动解仅有两类,而且给出了每一类非振动解存在的必要条件,同时也建立了方程振动的若干充分判据.
- 泛函微分方程 /
- 振动 /
- 非线性 /
- Lebesgue测度
Abstract: In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure.It is found thatthe nonoscillatory sclutions only have two kinds on some conditions only have And necessaryconditions for the existence of each kind of nonoscillatory solutions are presented as well. At the sameime. some sufficient conditions for oscillatory solutions are also established.
- functional differential equation /
- oscillation /
- nonlinear /
- Lebesgue measure

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