Bifurcation and Asymptotic Behavior of Solutions of a Delay-Differential Equation with Diffusion

1989 ◽  
Vol 20 (3) ◽  
pp. 533-546 ◽  
Author(s):  
Margaret C. Memory
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Delay Differential Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Differential

Some Asymptotic Properties of Solutions of a Neutral Delay Equation With an Oscillatory Coefficient

1993 ◽  
Vol 36 (3) ◽  
pp. 263-272 ◽  
Author(s):  
John R. Graef ◽  
Paul W. Spikes
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Delay Differential Equation ◽  
Asymptotic Properties ◽  
Delay Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Delay Differential

AbstractThe authors consider the nonlinear neutral delay differential equationand obtain results on the asymptotic behavior of solutions. Some of the results require that P(t) has arbitrarily large zeros or that P(t) oscillates about — 1

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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