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Keywords:
neutral equation; asymptotic behavior
neutral equation; asymptotic behavior
Summary:
In this paper we study asymptotic behavior of solutions of second order neutral functional differential equation of the form \[ \Big (x(t)+px(t-\tau )\Big )^{\prime \prime }+f(t,x(t))=0\,. \] We present conditions under which all nonoscillatory solutions are asymptotic to $at+b$ as $t\rightarrow \infty $, with $a,b\in R$. The obtained results extend those that are known for equation \[ u^{\prime \prime }+f(t,u)=0\,. \]
References:
[1] Bellman, R.: Stability Theory of Differential Equations. McGraw-Hill, London, 1953. MR 0061235 | Zbl 0053.24705
[2] Bihari, I.: A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta Math. Acad. Sci. Hung. 7 (1956), 81–94. MR 0079154 | Zbl 0070.08201
[3] Cohen, D. S.: The asymptotic behavior of a class of nonlinear differential equations. Proc. Amer. Math. Soc. 18 (1967), 607–609. MR 0212289 | Zbl 0152.28501
[4] Naito, M.: Integral averages and the asymptotic behavior of solutions of second order ordinary differential equations. J. Math. Anal. Appl. 164 (1992), 370–380. MR 1151041 | Zbl 0754.34045
[5] Philos, Ch. G., Purnaras, I. K.: Asymptotic behavior of solutions of second order nonlinear differential equations. Nonlinear Anal. 24 (1995), 81–90. MR 1308471
[6] Rogovchenko, Y. V.: On the asymptotic behavior of solutions for a class of second order nonlinear differential equations. Collect. Math. 49 (1998), 113–120. MR 1629766 | Zbl 0936.34037
[7] Rogovchenko, Y. V., Villari, G.: Asymptotic behavior of solutions for second order nonlinear autonomous differential equations. NoDEA- Nonlinear Differential Equations Appl. 4 (1997), 271–282. MR 1446220
[8] Tong, J.: The asymptotic behavior of a class of nonlinear differential equations second order. Proc. Amer. Math. Soc. 84 (1982), 235–236. MR 0637175
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