instability of solutions of certain nonlinear vector differential equations of order seven

Instability of Solutions of Certain Nonlinear Vector Differential Equations of Third Order

In this paper, study the system of differential equations ... X + F (Ẋ)Ẍ +G(X)Ẋ +H(X, Ẋ, Ẍ) = 0 . We find sufficient conditions for the zero solution to be unstable, and to be the only periodic solution.

Further Results on the Instability of Solutions of Certain Nonlinear Vector Differential Equations of Fifth Order

By using Lyapunov's second method [13], some new results are established, which insure that the zero solution of non-linear vector differential equations of the form is unstable.

Instability Results for Certain Third Order Nonlinear Vector Differential Equations

Our goal in this paper is to obtain sufficient conditions for instability of the zero solution to the non-linear vector differential equation ... X + F (X, Ẋ)Ẍ + G(Ẋ) + H(X) = 0. An example illustrates the results obtained.

Convergence of Solutions of Certain Fourth-Order Nonlinear Differential Equations

We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature. This is an open access article distributed under the Creative Commons Attribution Li...

Some Instability Results on Certain Third Order Nonlinear Vector Differential Equations

In this paper, we obtain some sufficient conditions under which the zero solution of a certain third order non-linear ordinary vector differential equation is unstable. Our results include and improve some well-known results exist in the literature.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS