A Note on a Boundedness Theorem for Some Third Order Differential Equations

Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations

“…Mathematical studies of third-order nonlinear ordinary differential equations include those of Tunç [10] who proved the stability and boundedness of solutions of nonlinear vector differential equations by means of Lyapunov's second method, Ezeilo [11][12][13], Rao [14], Reissig et al [15], Tunç and Ateş [16], etc. On the other hand, mathematical modelling of several physical phenomena sometimes result in third-order nonlinear ordinary differential equations.…”

Existence theory and stability analysis to a system of boundary value problem

“…Such systems are related to jerk type equations, which are mostly applicable in manufacturing processes. The stability analysis and boundedness of solutions to integer third-order nonlinear ordinary differential equations has been investigated vis using Lyapunov's second method by several authors, see [28][29][30][31]. For further applications of third order equations reader should see [32][33][34][35].…”

Asymptotic Behaviour of Solutions of Certain Second Order Non-Autonomous Nonlinear Ordinary Differential Equation

“…However, the construction of these Lyapunov functions remain a general problem due to lack of unique way for its construction. Many methods have been proposed in the literatures (see for instance [9], [10], [22], [23], [35], [25], [26], [12], [13], [14], [15], [16], [37], [36], [22], [23], [24], [19], [45], [29], [43], [44]).…”