On the stability and boundedness of solutions of a kind of third order delay differential equations

Abstract

Abstract. This paper studies the stability and boundedness of solutions of certain nonlinear third-order delay differential equations. Sufficient conditions for the stability and boundedness of solutions for the equations considered are obtained by constructing a Lyapunov functional.Mathematical subject classification: 34K20.

Stability and boundedness of solutions of a kind of third-order delay differential equations

“…14]). In recent year, many books and papers dealt with the delay differential equation and obtained many good results, for example, [1,2,3,18,19,21], etc. In many references, the authors dealt with the problems by considering Lyapunov functions or functionals and obtained the criteria for the stability and boundedness.…”

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, 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.…”