Construction Of Lyapunov Functions For Some Fourth Order Nonlinear Ordinary Differential Equations By Method Of Integration

Abstract In giving adequate attention to some qualitative properties of solutions in ordinary differential equations Lyapunov functions is quite indispensable. The process of tackling some problems in the application is the construction of appropriate Lyapunov functions for some nonlinear fourth order differential equation. Our focus is finding Vx a quadratic form and positive definite also finding Ux which is positive definite such that the derivative of V with respect to time would be equal to the negative value of Ux In this work we adopted the pre-multiplication of the given differential equation by and thereafter we integrated with respect to form to . We obtained a Lyapunov function candidate for a fourth order differential equation or its scalar equation.