Asymptotic Periodicity, Monotonicity, and Oscillation of Solutions of Scalar Neutral Functional Differential Equations

✍ Scribed by T. Krisztin; J. Wu

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 266 KB
• Volume: 199
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.0158

✦ Synopsis

We consider the periodic scalar neutral functional differential equation Ž .w Ž . Ž . Ž .x Ž Ž .. Ž Ž .. drdt x t y c t x t y s yh t, x t q h t y , x t y , where c is continuously differentiable, h is increasing in its second argument, and both c and h are 1-periodic in the t-variable. The two time-lags and are not required to be Ž . the same. It is shown that, under certain conditions, i the set of 1-periodic solutions is an ordered arc and each solution is convergent to a periodic solution; Ž .

ii the asymptotic and oscillatory behaviors of each solution are completely classified in terms of the value of the first integral at the initial condition.