scholarly journals On asymptotic behavior of solutions to higher-order sublinear Emden–Fowler delay differential equations

2017 ◽  
Vol 67 ◽  
pp. 53-59 ◽  
Author(s):  
Tongxing Li ◽  
Yuriy V. Rogovchenko
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Higher Order ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Differential

scholarly journals Asymptotic behavior for a class of delay differential equations with a forcing term

2003 ◽  
Vol 34 (4) ◽  
pp. 309-316
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Forcing Term ◽  
Delay Differential ◽  
T Tau

We study the asymptotic behavior of solutions of the following forced delay differential equation $$ x'(t)=-p(t)f(x(t-\tau))+r(t),\quad t\ge 0.  \eqno{(*)}$$ It is show that if $ f$ is increasing and $ |f(x)|\le |x|$ for all $ x\in R$, $ \lim_{t\to +\infty} {r(t)\over p(t)}=0$, $ \int_0^{+\infty} p(s)ds=+\infty$ and $ \limsup_{t\to+\infty} \int_{t-\tau}^t p(s)ds

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