THE UNIQUENESS OF THE SOLUTION OF LIENARD SYSTEM TO THE INITIAL VALUE PROBLEM

1 IntroductionThe Li6nard systemis a very important nonlinear system. Many authors have studied the asymptotic behavior of its solutions. But for this purpose we require first the uniquenessof its solutions to the initial value problem. Most references did not discuss itin detail, they generally assume that F(x) and g(x) are continuous and satisfythe conditions for the uniqueness of the solution. Only few authors gave someconcrete conditions.FOr example Dragilev [1] required that F(x) and g…     

纠正《高等数学》(同济四版)的一个错误

《高等数学》[1]中关于两类曲线积分关系的推导是错误的 .关于两类曲线积分关系有一个熟知的公式 ,即∫LP(x,y) dx+Q(x,y) dy=∫L [P(x,y) cosα+Q(x,y) cosβ]ds,(1 )其中 cosα,cosβ为有向弧段 L的切向量的方向余弦 .但《高等数学》中关于 (1 )的推导是错误的 .它给出曲线弧 L的参数方程x=φ(t) ,　 y=ψ(t) (2 )(注意从 (2 )中体现不出弧的方向 ) ,它又假定有向弧起点和终点的参数分别为 α和 β,然后下式成立∫LP(x,y) dx+Q(x,y) dy=∫βα {P[φ(t) ,ψ(t) ]φ′(t) +Q[φ(t) ,ψ(t) ]ψ′(t) }dt. (3)它又设有向弧切向量为t={…