Instability of Certain Nonlinear Stochastic Differential Equations

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.

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

sufficient conditions are established under which the zero solution x = 0 of equation (2) isunstable.

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 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.

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