Stability and boundedness criteria of solutions of a certain system of second order differential equations

On uniform-ultimate boundedness and periodicity results of solutions to certain second order non-linear vector differential equations

“…The works of Omeike et.al. [25], Adeyanju [5] and above listed papers gave us motivation for the present work.…”

“…(1.1). In a recent paper, Adeyanju [5] proved some results on the stability and boundedness of solutions to (1.1) using a complete Lyapunov function. The works of Omeike et.al.…”

Boundedness of Vector Linéard Equation with Multiple Variable Delays

“…As for the motivation of this article, recently, Adeyanju [13] and Adeyanju and Tunç [14] considered the following n-dimensional ODEs of second order without delay and with the constant delay τ, respectively:…”

“…Adeyanju [13] discussed boundedness, uniformly boundedness and some other behaviors of solutions of the first ODE via the Lyapunov second method. 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.…”

“…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].…”