In this paper, we studied the half inverse spectral problem for singular diffusion operator with certain boundary conditions. The discontinuity function in this operator is defined as and α > 0, α ≠ 1, β > 0, β ≠ 1 and a₁, a₂ ∈ (0, π), , . We prove that the potential functions p(x) and q(x) are determined uniquely by using the Yang–Zettl and Hocstadt–Lieberman methods. We examine that if potential functions q(x) and p(x) are prescribed over the interval , then reconstruction of the potential functions q(x) and p(x) by one spectrum on the (0, π).

中文翻译：

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具有一定边界条件的奇异扩散算子的半逆问题

本文研究了具有一定边界条件的奇异扩散算子的半逆谱问题。该算子中的不连续函数定义为且α  > 0, α  ≠ 1, β  > 0, β  ≠ 1 和a ₁ , a ₂  ∈ (0,  π ), , . 我们证明了势函数p ( x ) 和q ( x ) 是使用 Yang-Zettl 和 Hocstadt-Lieberman 方法唯一确定的。我们检查如果势函数q ( x ) 和p( x ) 在区间 上规定，然后通过 (0, π )上的一个谱 重建势函数q ( x ) 和p ( x )。