Construction of Lyapunov Functions for the Stability of Fifth Order Nonlinear Ordinary Differential Equations

This study employed Lyapunov function method to examine the stability of nonlinear ordinary differential equations. Using direct Lyapunov method, we constructed Lyapunov function to investigate the stability of fifth order nonlinear ordinary differential equations. V(x), a quadratic form and positive definite and U(x) which is also positive definite was chosen such that the derivative of V(x) with respect to time would be equal to the negative value of U(x). We adopted the pre-multiplication of the given equation by x... and obtained a Lyapunov function which established local and global stability of a fifth order differential equation.