Sturm分离定理的逆定理
The converse of Sturm's Separation Theorem
摘要：
我们表明，Sturm的经典分离定理的交错的零点的线性无关的解决方案的实二阶两项常微分方程必然失败的存在下，一个独特的转折点的主部的方程。相关结果进行了讨论。最后一节包含的主要结果的一个有限数量的转折点的延伸。
英文摘要：
We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a unique turning point in the principal part of the equation. Related results are discussed. The last section contains an extension of the main result to a finite number of turning points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
