中文摘要：

该文研究有限区间上一般自伴边界条件下的Sturm-Liouville方程的逆特征值问题.将Neumann边界条件下Sturm-Liouville方程的Ambarzumyan型定理推广到一般自伴边界条件下情形,证明了如果它的特征值与零势的特征值一样,则Sturm-Liouville方程的势为零.

英文摘要：

This paper deals with the inverse eigenvalue problems for the Sturm-Liouville equation on finite interval with general self-adjoint boundary conditions.The authors extend the classical Ambarzumyan＇s theorem for the Sturm-Liouville equation with Neumann boundary conditions to the general self-adjoint boundary conditions.They prove that if the spectrum is the same as the spectrum belonging to the zero potential and the potential possesses an integral condition,then the potential is actually zero.