On the asymptotic behavior of the solutions of third order delay differential equations

Abstract

By constructing a Lyapunov functional, we obtain some sufficient conditions which guarantee the stability and boundedness of solutions for some nonlinear differential equations of third order with delay. Our result improve and generalize existing results in the relevant literature of nonlinear third order differential equations.

Boundedness and square integrability of solutions of certain third-order differential equations

“…al. [11], a survey book and Afuwape [1], [2], Graef [4], [5], Qian [9], [10], Omeike [6]- [8], Remili [12]- [20], Sadek [21], Tunç [22]- [27], Zhu [28] and the references cited therein, to mention few.…”

Stability and ultimate boundedness of solutions of some third order differential equations with delay

“…By employing the Lyapunov's method, many good and interesting results have been obtained concerning the boundedness, ultimate boundedness and the asymptotic stability of solutions for certain nonlinear differential equations. See, the papers of ; ; Burton (2005); Hara (1971); Bao and Cao (2009); Pan and Cao (2010, 2011, 2012; Omeike (2010); Oudjedi et al (2014); Remili and Beldjerd (2014); ; Remili and Damerdji Oudjedi (2014); Li and Lizhi (1987); Tunc¸(2007aTunc¸( , b, 2010; Yoshizawa (1966) and their references.…”

Boundedness and stability in third order nonlinear vector differential equations with multiple deviating arguments

“…In the last years, there has been increasing interest in obtaining the sufficient conditions for the stability/instability/ boundedness/ ultimately boundedness etc. The problem of the boundedness and stability of solutions of vector differential equations has been widely studied by many authors, who have provided many techniques especially for delay differential equations, for some related contributions, we refer the reader to Graef et al (2015a,b), Oudjedi et al (2014), Remili and Beldjerd (2014), Oudjedi (2014a,b, 2016a,b,c,d,e), Remili et al (2016), Tunc¸(2006a,b), Tunc¸and Go¨zen (2014), Zhengxin et al (2010aZhengxin et al ( ,b, 2015, Jinde (2005, 2007). In the following, we provide some background details regarding the study of various classes of third differential equations.…”