Boundedness of solutions of certain third order differential equation

Abstract

Abstract. We study the behavior of the solutions of the differential equation. We shall present sufficient conditions on the functions involved under which the solutions of the above differential equation are bounded. Some results on the regularity and asymptotic behavior of the solutions are also obtained.Mathematics subject classification (1991): 54C25.

Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order

“…Differential equations of third order are valuable tools in the modeling of many phenomena in various fields of science and engineering (Chlouverakis and Sprott [1], Cronin-Scanlon [2], Eichhorn et al [3], Friedrichs [4], Linz [5], and Rauch [6]). In reality, the stability and boundedness of solutions of certain nonlinear differential equations of the third order have been received intensive attentions by authors (Ademola et al [7], Afuwape and Castellanos [8], Chukwu [9], Ezeilo ( [10,11]), Hara [12], Mehri and Shadman [13], Ogundare and Okecha [14], Omeike [15], Reissig et al [16], Swick [17], Tejumola ([18,19]), Tunç [20][21][22][23][24][25][26][27][28][29][30][31][32][33], and Yoshizawa [34]).…”

Bounded solutions to nonlinear delay differential equations of third order

“…We establish here some sufficient conditions which guarantee to the boundedness of solutions of (1.2). Obviously, equations investigated by Mehri and Shadman [2] and Tunç [3] are special case of our equation (1.2).…”

“…In 1999, Mehri and Shadman [2] considered third order nonlinear differential equation without delay:…”

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)).…”