Some Instability Results on Certain Third Order Nonlinear Vector 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.

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

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.

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

Nonstandard explicit third-order Runge-Kutta method with positivity property

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...