A Uniqueness Theorem for Sturm-Liouville Operators with Eigenparameter in Boundary Conditions

摘要

This paper establishes a uniqueness theorem for a kind of Sturm-Liouville problem. For a fixed index n (n E Z), it is shown that the n-th eigenvalue λ_n(q, a) of the Sturm-Liouville problem is strictly monotonous in a. If the spectral set {λ_n(q, αk)}_(k=1)~(+∞) can be measured for distinct α_k, then the potential q(x) on the interval [0, π] can be uniquely determined by the spectral set {λ_n(q, α_k)}_(k=1)~(+∞).