具有后效的逆Sturm-Liouville问题的唯一性

摘要

考虑具有后效的Sturm-Liouville逆特征值问题,即带有分离型自伴边界条件的一类积-微分方程.该文证明,当势函数及部分区间上的核函数为已知时,整个区间上核函数能够通过部分特征值完全确定.%The inverse eigenvalue problem of an integro-differential equation with self-adjoint boundary conditions is considered, which may be also regarded as a perturbation of the classical potential equation. Some uniqueness results are obtained which imply that the kernel function M can completely be determined even if only partial information is given on M together with partial information on one full spectrum, when the potention function is known.