Stability and boundedness of a kind of third-order delay differential system

On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument

“…Such equations are frequently encountered as mathematical models of most dynamical processes in mechanics, control theory, physics, chemistry, biology, medicine, economics, atomic energy, information theory, etc. Especially, since 1960s, many good books and papers have been published and are still being published on the delay differential equations (see, for example, Burton [1,2], Burton and Zhang [3], Èl'sgol'ts [4], Èl'sgol'ts and Norkin [5], Gopalsamy [6], Hale [7], Hale and Verduyn Lunel [8], Kolmanovskii and Myshkis [9], Kolmanovskii and Nosov [10], Krasovskii [11], Sadek [15], Sinha [16], Tejumola and Tchegnani [17], Tunç [19,20,[22][23][24][25], Yoshizawa [26], Zhu [27] and the references thereof). It is also worth mentioning that the use of the Lyapunov direct method [12] for equations with delays encountered some principal difficulties.…”

Uniform Ultimate Boundedness of Solutions of Third-Order Nonlinear Delay Differential Equations

“…The most effective method to study the uniform boundedness and uniform ultimate boundedness of (1.1) is the Lyapunov's direct (or second) method. See [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein. Thus, by using a more general Lyapunov function, our result improves some known results in [12] and [15], and revise a result in [14].…”

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

“…Many interesting results, on the qualitative behavior of solutions of the third order differential equations have been obtained by Omeike [4,5], Remili and Oudjedi [7], Sadek [8,9], Tunç [11,12,13,14] and Zhu [17] and references therein.…”