ON THE STABILITY OF SOLUTIONS OF A CERTAIN GENERAL THIRD ORDER NON LINEAR ORDINARY DIFFERENTIAL EQUATION

This Work Deals With The Stability Of Solutions Of The Nonlinear Third Order Autonomous Ordinary Differential Equationx ⃛+f(x,x ̇)x ̈+g(x) x ̇+h(x)=0. The Main Object Of This Paper Is To Establish Sufficient Conditions For The Asymptotic Stability Of The Trivial Solution x ̅ = 0 ̅ By Constructing A Suitable Liapounov Functional

Keywords: Stability; Trivial Solution; Liapounov Functional; Positive Definite; Negative Definite.