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IJSTR >> Volume 3- Issue 10, October 2014 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

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

[Full Text]



Orie Bassey O.



Index Terms: Lyapunov Functions, Linear systems, non linear systems Negative definite, Positive definite, Linear and non linear systems



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 V(x), a quadratic form and positive definite also finding U(x) which is positive definite such that the derivative of V with respect to time would be equal to the negative value of U(x) 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.



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