On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays

Improved Stability and Instability Results for Neutral Integro-Differential Equations including Infinite Delay

“…On the other hand, as for some other qualitative results with regard to IDEs with and without delay(s), however not with regard to NVIDEs, one can find numerous results in papers of Bohner et al [5], Bohner and Tunç [24], Burton and Mahfoud [6], Chang and Wang [7], Eloe et al [9], Funakubo et al [10], Gözen and Tunç [12], Graef and Tunç [13], Qian [26], Staffans [27], Taie and Bakhit [28], Tunç [29][30][31], Tunç and Tunç [32,33], Tunç et al [34,35], Vanualailai and Nakagiri [36], Wang [37], Wang et al [38], Xu [39], Zhang [43,44] , the references of these papers and the books of Lakshmikantham and Rama Mohana Rao [19], Volterra [42]. In these papers, the main results have been proved via the LKF method or Lyapunov's function method.…”

Boundedness of Vector Linéard Equation with Multiple Variable Delays

“…Next, Adeyanju and Tunç [14] constructed suitable new sufficient conditions that allow for the uniform ultimate boundedness of solutions of the second ODE with constant delay via the LKF method as a basic tool. On the other hand, we would like to outline some related works as follows: the stability and boundedness of solutions of vector differential equations by Lyapunov's second method (see [13,[15][16][17][18][19][20]), qualitative behavior of ordinary and functional differential equations (see [2,21]), stability, boundedness and periodicity of solutions of delay differential equations of second order (see [22][23][24]) and existence, uniqueness, stability, etc., of ordinary and functional differential equations (see [12]); for some other results, see [1,14,25,26].…”

“…This case is also a novelty. Furthermore, in the papers of Ademola et al [22], Adeyanju and Adams [15], Omeike et al ( [16,17]), Tunç [23,26], Tunç and Tunç [19,24] and Tunç et al [28], the boundedness and some other qualitative behaviors of solutions of certain scalar and vector ODEs of second order with or without delay have been investigated, and several interesting results have been obtained in these papers. It can be checked that the ODEs of second order of these papers are particular cases of the ODE (3) of second order, or they are included by the ODE (3) of second order for some particular choices of them.…”

On the Admissibility of Nonlinear Singular Systems With Time-Varying Delays Abdullah Yigit and Cemil Tunc

“…Motivated by above discussions and [8][9][10][11], in this article, we consider the problem of asymptotic admissibility of nonlinear singular systems with two time-varying delays. By defining new LKFs, new asymptotic admissibility conditions, which guarantee the regularity, impulse-free and asymptotic stability, are established in terms of the matrix inequality technique.…”