【摘要】 对于常系数齐线性微分方程组ddXt=AX,当A的特征根λi的重数ni 1时,特征根λi所对应解X(t)=(P1(t),…,Pn(t))Teλit中,t的多项式p(ji)(t)的次数ni+秩(A-λiE)-n,改进了多项式p(ji)(t)的次数ni-1的估计式.更多还原

【Abstract】 To the linear homogeneous differential equation with constant coefficients dXdt=AX,when the number of repetition niof the eigenvalue λi of A is bigger or equal of 1,the number of times of polynomial pj(t)(j=1,…,n) is less or equal of ni+rank(A-λiE)-n in the corresponding solution X(t)=(P1(t),…,Pn(t))Teλit of λi.So the conlusion which the number of times of pj(t) is less or equal of ni-1 is improved.更多还原