Sturm-Liouville问题的特征值对势函数的依赖性

Dependence of eigenvalues of Sturm-Liouville problems on the potential function

研究了定义在[0,1]上的Sturm-Liouville问题的特征值对势函数的连续依赖性.应用比较定理和定义区间单调性证明了:当部分区间[x0,1]上的势函数趋于无穷大时,[0,1]区间上的特征值渐进趋近于[0,x0]区间上的某个特征值.推广了一些作者对Sturm-Liouville问题研究的相应结果,并为其相应问题的研究提供了一个新的视角.

This paper studies mainly the eigenvalues of Sturm-Liouville （SL） problems definded in [0, 1] dependent contiuously on the potential function. By the comparison theorem and domain mouotonicity, it proves that when the potential function in the interval [x0, 1] tends to infinity, the eigenvalues in the interval [0, 1] asymptotically approach the eigenvalues in the interval [0, x0]. It promotes the corresponding results of Sturm-Liouville problems which some authors studies, and provides a new angle of view.