Necessary and sufficient conditions for the oscillatory and asymptotic behaviour of solutions to neutral delay dynamic equations

Electronic Journal of Differential Equations

卷:2009

关键词: Asymptotic behavior;    neutral dynamic equations;    nonoscillation;    oscillation;    time scale;   

DOI  :  

来源: DOAJ

【 摘 要 】

This article concerns the asymptotic behaviour of solutions to nonlinearfirst-order neutral delay dynamic equations involving coefficientswith opposite signs. We present necessary and sufficient conditions forthe solutions to oscillate or to converge to zero.The coefficient associated with the neutral part is considered inthree distinct ranges, in one of which the coefficient is allowedto oscillate. Illustrative examples show that the existing resultsdo not apply to these examples and hence they show the significanceof our results. The results of this article are also new for theparticular choices of the time scale $mathbb{T}=mathbb{R}$ and$mathbb{T}=mathbb{Z}$.

【 授权许可】

Unknown