Bound of solutions to third-order nonlinear differential equations with bounded delay

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]).…”

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

“…However, with respect to our observations in the literature, until now, many good results especially dealt with the stability and bounded of solutions of nonlinear third order differential equations without delay (see, for example, the book of Reissig et al [6], the papers of Tunç [8][9][10][11], Tunç and Ateş [19], and the references thereof). Besides, it is worth mentioning that to the best of our knowledge, in spite of the existence of many papers on the stability and bounded of solutions of nonlinear third order differential equations without delay, we found the papers of Sadek [7] and Tunç [12,[14][15][16][17][18] on the stability and boundedness of solutions to autonomous and non-autonomous third order differential equations with delay. Namely, first, in 2005, Sadek [7] discussed the asymptotic stability of the solution x = 0 to the following non-autonomous third order differential equation with constant delay, r :…”

“…This work is the first attempt in the literature on the bounded of solutions of non-autonomous third order differential equation with delay, (2), when a(t) = 1, b(t) = 1 and c(t) = 1. The motivation for the present work has been inspired basically by the papers of Sadek [7] and Tunç [12][13][14][15][16][17][18][19]. Throughout all foregoing papers, the Liapunov's second (or direct) method [5] has been used as a main tool to carry out the proofs of the main results thereof.…”

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.…”