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

Abstract

In this paper, a class of non-linear vector differential equations of third order with delay is considered. The stability, boundedness and ultimately boundedness of solutions are studied. The technique of proofs involves defining an appropriate Lyapunov functional. The obtained results include and improve the results in the literature.

A note on the stability and boundedness of solutions to non-linear differential systems of second order

“…(3) is guaranteed. In particular, for the existence and uniqueness of solutions and some qualitative properties of solutions, we can refer to (Tunc¸, 2010(Tunc¸, , 2017Song et al, 2011;Wang et al, 2010a,b).…”

Uniform Ultimate Boundedness Results for some System of Third Order Nonlinear Delay Differential Equations

“…However, there are few papers in connection with the qualitative properties of solutions of systems of third order nonlinear delay differential equations in literature. Recently, in [12], equation (1.1) in which r = r(t), H ∈ C ′ (R n ) and P (t, X, Ẋ, Ẍ) = P (t) was investigated for the boundedness of solutions, while in [17], the author studied the stability and boundedness of solutions of the equation…”

A Stability Result for the Solutions of a Certain Fourth-Order Vector Differential Equation with Delay

“…Over the past years, many new results have been obtained on the stability for solutions of ordinary and functional differential equations of higher order without and with delay. For instance, we draw the attention of the interested reader to the book by Reissig et al [10] and the papers by Abou El-Ela et al [1,2,3], Adesina et al [4], Omeike [8,9], Sadek [11], Tunç [12,13,14] and the references cited therein. As far as we know, researches that discussed the stability of solutions to vector differential equations can briefly be summarized as follows:…”