【摘要】 本文找到了方程属极限圆的用系数表示的充要条件 ,并给出了比较容易验证的充分条件 ,改进了已有的结果 .更多还原

【Abstract】 In this article we will consider the homogeneous difference equation -(c nΔu n)=(λ a n+b n)u n,n≥0 where {a n}∞ 0,{b n}∞ 0 and {c n}∞ -1 are sequences of real numbers satisfying c n≠0,a n>0,n≥0.In 1909,H.Weyl pointed out that each second order linear differential equation belongs to one of two alternative classes depending on whether all its slutions are square integrable.If so,the equation is called of the Limit-Circle(L.C.)type,and otherwise the Limit-Point(L.P.)type.This paper is concerned with the discrete version of Weyl’s alternative theorem for the difference equation (1) to be of L.C.or L.P. type.Necessary and sufficient conditions for (1) to be of the L.C.type are obtained.These results improve and extend some previous results.更多还原