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

Abstract

We consider a nonautonomous functional differential equation of the third order with multiple deviating arguments. Using the Lyapunov-Krasovskiì functional approach, we give certain sufficient conditions to guarantee the asymptotic stability and uniform boundedness of the solutions.

Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

“…Obviously, the equations discussed in [5] and [15], are particular cases of our equation (2). Here, by this work, we improve the boundedness result obtained in [5,15].…”

“…Recently, in 2013 Tunç and Gözen [15] considered the non autonomous differential equation of the third order with multiple deviating arguments:…”

“…In this work, we want to adopt the approach in Omeike [5] and Tunç [15] to extend the result in Swick [10] to the equation (1) and give sufficient criteria which guarantee the existence of uniform asymptotic stability of the solution with their derivatives on the real line. Obviously, the equations discussed in [5] and [15], are particular cases of our equation (2).…”

Boundedness and stability in third order nonlinear differential equations with multiple deviating arguments

“…Finally, in 2013 Tunç and Gözen [30] discussed conditions for stability and uniform boundedness of solutions of equation (12)…”

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

“…In this regard, we can mention the works of Burton [1,2], Driver [3], Hale [4], and Yoshizawa [5,6] which contain general results on the subject matters and expository papers of Abou-El-Ela et al [7], Ademola et al [8][9][10], Adesina [11], Afuwape and Omeike [12], Chukwu [13], Gui [14], Omeike [15,16], Sadek [17], Tejumola and Tchegnani [18], Tunç et al [19][20][21][22][23][24][25][26][27][28], Yao and Wang [29], and Zhu [30] and the references cited therein.…”