Stability and bounded of solutions to non-autonomous delay differential equations of third order

Abstract

In this paper, we obtain some sufficient conditions to guarantee the uniform asymptotic stability of zero solution and bounded of all solutions to nonautonomous delay differential equation of third order ...when p(t, x(t), x(t − r),ẋ(t),ẋ(t − r),ẍ(t)) = 0 and p(t, x(t), x(t − r),ẋ(t),ẋ(t − r),ẍ(t)) = 0, respectively. By using the Liapunov functional approach, we prove two new results on the subject.

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

“…This case is the novelty of the present paper. It should also be noted that the results to be established here are different from those in Tunç [20][21][22][23][24][25][26][27][28][29][30][31][32][33] and the literature.…”

“…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]).…”

On the stability and boundedness of a class of higher order delay differential equations

“…It also follows that the equation studied here, Eq. (1), is different from that investigated in [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Finally, throughout all the above papers, the coefficient of the second term x 00 (t) in Eq.…”

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.…”