On the asymptotic behavior of solutions of certain differential functional equations

✍ Scribed by O.C. Oliveira Filho

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 540 KB
• Volume: 30
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(97)00457-4

✦ Synopsis

We investigate the asymptotic behavior, the oscillatory character and the periodic nature of solutions of the retarded and advanced equation

where the argument deviation is given by r(t) = t -2[3 Here, [.] denotes the usual "greatest-integer map". And, besides discussing explicit conditions for such behavior, as the ones obtained by Cooke and Wiener in [4] and 151, we also introduce a more recent result by Oliveira Filho and Carvalho ((9,101). Al so, we give a set of necessary and sufficient condictions for the existence of certain types of periodic solutions of the equation above to the particular case r(t) = 1, i.e., the parameter family of scalar differential-difference equation S(t) = ml?(t) + bz(t -l), where we restrict attention to solutions with integral period: 7 = 3,4,5,.