Global Asymptotic Stability Of A Class Of Four Order Nonlinear Differential Equation

By researching the Lyapunov function for four order linear differential equationwith constant coefficients, The thesis discusses two kinds of the construction methodsof Lyapunov functions of four order nonlinear differential equations, the energymetric algorithm and the method of analogy, and obtains global asymptotic stabilityand instability sufficient conditions of some class of four order nonlinear differentialequations by using the Lyapunov the proposed function.This thesis is divided into four parts:The first part introduces the research background and significance of the stabilitytheory, and gives the basic concepts and theorems of the Lyapunov stability.The second part introduces how to construct Lyapunov function by using theenergy metric algorithm and the method of analogy, by researching the Barbashinformula of Lyapunov function of linear differential equation with constantcoefficients.The third part gives the global asymptotic stability of nonlinear autonomousdifferential equation theorem by constructing appropriate Lyapunov functions fordifferent differential equation.The fourth part further discusses of the nature of four order nonlinear nonautonomous differential equations, and gives the globally asymptotic stability of thezero solution and sufficient conditions for the stability.