三阶半线性时滞微分方程的振动性和渐近性

林全文,俞元洪

系统科学与数学 ›› 2015, Vol. 35 ›› Issue (2) : 233-244.

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PDF(286 KB)
系统科学与数学 ›› 2015, Vol. 35 ›› Issue (2) : 233-244. DOI: 10.12341/jssms12534
论文

三阶半线性时滞微分方程的振动性和渐近性

    林全文1,俞元洪2
作者信息 +

OSCILLATORY AND ASYMPTOTIC PROPERTIES FOR THIRD ORDER HALF-LINEAR DELAY DIFFERENTIAL EQUATIONS

    LIN Quanwen1 , YU Yuanhong2
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摘要

虑三阶半线性时滞微分方程 ([x(t)]α)+q(t)xα(σ(t))=0,tt0,\eqno() 其中q(t)是正函数, α>0是奇正整数之商,时滞函 数0<σ(t)t, σ(t)>0满足limtσ(t)=. 文章建立了保证方程()振动或者解收敛到零的Hille型和 Nehari型充分条件.文章的结果即使在时滞不存在的情况也是新的.为说明主要结果给出了例子.

Abstract

The objective of this paper is to study the oscillation and asymptotic behavior of the third order half-linear delay differential equation ([x(t)]α)+q(t)xα(σ(t))=0,tt0,\eqno() where q(t) is a positive function, α>0 is a quotient of odd positive integers and the delay function 0<σ(t)t, σ(t)>0  satisfies limtσ(t)=. We establish some sufficient conditions of Hille and Nehari type, which ensure that () is oscillatory or the solutions converge to zero. Our results are new even in the nondelay case. Some examples are considered to illustrate the main results.

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林全文 , 俞元洪. 三阶半线性时滞微分方程的振动性和渐近性. 系统科学与数学, 2015, 35(2): 233-244. https://doi.org/10.12341/jssms12534
LIN Quanwen , YU Yuanhong. OSCILLATORY AND ASYMPTOTIC PROPERTIES FOR THIRD ORDER HALF-LINEAR DELAY DIFFERENTIAL EQUATIONS. Journal of Systems Science and Mathematical Sciences, 2015, 35(2): 233-244 https://doi.org/10.12341/jssms12534
中图分类号: 34K11    34C10   
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