The present paper is concerned with the spectral theory of nonlocal Sturm–Liouville eigenvalue problems on a finite interval. The continuity, differentiability and comparison results of eigenvalues with respect to the nonlocal potentials are studied, and the oscillation properties of eigenfunctions are investigated. The comparison result of eigenvalues and the oscillation properties of eigenfunctions indicate that the spectral properties of nonlocal problems are very different from those of classical Sturm–Liouville problems. Some examples are given to explain this essential difference.

中文翻译：

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非局部Sturm-Liouville问题的特征值和特征函数的性质

本文涉及有限区间非局部Sturm-Liouville特征值问题的谱理论。研究了特征值相对于非局部电位的连续性，可微性和比较结果，并研究了特征函数的振动性质。特征值和特征函数的振动特性的比较结果表明，非局部问题的谱特性与经典Sturm–Liouville问题的谱特性非常不同。给出了一些例子来解释这种本质的区别。