A half‐inverse problem for singular diffusion operator with certain boundary conditions

Abstract

AbstractIn 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).