研究了一类不连续的Sturm—Liouville问题在开区间(a,c)∪(c,b)上特征函数的振动性,构建了一个与其相关的新的Hilbert空间,证明了具有分离边界条件的这类问题的第n个特征值λn(n=1,2,…)所对应的特征函数在区间(a,c)∪(c,b)上恰有n-1个零点.
Oscillation characterizations for eigenfunctions of a class of discontinuous Sturm-Liouville problems are investigated in a open interval (a, c) ∪ (c, b). A new Hilbert space is defined. We show that any eigenfunction for An (n = 1, 2,…) has exactly n - 1 zeros in the interval (a, c) ∪ (c, b).