摘要
下述方程组称为Dirac方程组: 其中λ为特征参数.设分别为方程组满足以下初值条件的特解,记.本文的主要。结果如下:Dirac方程组有π周期解等价于△(λ)=2,其一切解为π周期解等价于Dirac方程组有2π周期解等价于△(λ)=-2,其一切解为2π周期解等价于△(λ)=-2,y_(12)(π,λ)=y_(21)(π,λ)=0.
Following system of equations is called Dirac system of equationsy'2-[λ+p(x)]y1= 0 , y'1+[λ+r(x)]y2=0 ,where λ is eigen-parameter. Let us suppose Y1(x,λ)=(y11(x,λ),y12(x,λ))T and Y2(x,λ)=(y21(x,λ),y22(x,λ))T arc Cauchy solutions of the system of equations which satisfy following conditions res,pectivly:Y1(0,λ) = (1 ,0)T, Y2(o,λ) = (0, 1)T.Note △(λ)=y 11(π ,λ) + y22(π ,λ). Major results of this paper arc following. The Dirac system of equations has a π periodic solution iff △(λ) = 2, all solutions arc π periodic solutions iff △(λ)=2, y12(π , λ) = y 21 (π,λ) = 0; The Dirac system of solutions has a 2 π periodic solution iff △(λ)=-2 , all solutions arc 2 n periodic solutions iff △(λ)=-2, y 12(π,λ) = y 21(π,λ) = 0.
出处
《河南大学学报（自然科学版）》
CAS
1991年第2期51-54,共4页
Journal of Henan University:Natural Science
