On the stability and boundedness of certain third order non-autonomous differential equations of retarded type

Abstract

In this paper, based on the Lyapunov-Krasovskii functional approach, we obtain sufficient conditions which guarantee stability, uniformly stability, boundedness and uniformly boundedness of solutions of certain third order non-autonomous differential equations of retarded type. Our results complement and improve some recent ones. Subjclass :[2010]34K20.

Asymptotic stability of solutions for a kind of third-order stochastic differential equations with delays

“…In this direction, many authors have proposed different approaches to investigate the stability of solutions of third-order DDEs. We can mention the papers of Ademola et al [4,5], Graef and Tunç [8], Mahmoud [11], Omeike [17], Oudjedi et al [18], Remili et al [20,21], Sadek [23], Shekhar et al [24], Tunç [25][26][27][28][29] and the references cited therein.…”

Permutation Groups and Periodicity of Systems of Difference Equations

“…Hence, many papers dealt with the (QBSs)of higher order (DDEs) with (a or multiple) time lag(s) and obtained many interesting results by means of this theory, see, for example, the papers given in [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21] and the references cited therein to mention few). In deed, the many authors focused on (QBSs) of different models of (SDEs) and they got numerous interesting results over the last few years (see, for example, [22], [23], [24], [25], [26], [27]) and the references therein.…”

Stability and boundedness in delay system of differential equations of third order

“…During the last years, many good results have been obtained on the qualitative behaviors in ordinary and functional differential equations of third order without and with delay. In particular, for some works on the stability and boundedness in scalar ordinary and functional differential equations of third order without and with delay, we referee the interested reader to the papers of Ademola et al (2015), Ademola and Arawomo (2011), Afuwape and Castellanos (2010), , Graef and Tunc (2015), Mehri and Shadman (1999), Meng (1993), Omeike (2014), Omeike and Afuwape (2010), Qian (2000), Remili and Oudjedi (2014), Tunc (2004Tunc ( , 2005aTunc ( ,b,c, 2007Tunc ( , 2009aTunc ( ,b, 2010aTunc ( ,b, 2013aTunc ( ,b, 2014Tunc ( , 2015, Tunc and Mohammed (2014), Tunc and Ates ß (2006), Zhang and Yu (2013) and their references. However, to the best of our knowledge from the literature, by this time, little attention was given to the investigation into the stability/boundedness/ultimately boundedness in vector functional differential equations of third order with delay (see Tunc and Mohammed (2014)).…”