Uniqueness Properties of The Solution of The Inverse Problem for The Sturm-Liouville Equation With Discontinuous Leading Coefficient

Abstract

The present paper studies uniqueness properties of the solution of the inverse problem for the SturmLiouville equation with discontinuous leading coefficient and the separated boundary conditions. It is proved that the considered boundary-value is uniquely reconstructed, i.e. the potential function of the equation and the constants in the boundary conditions are uniquely determined by given Weyl function or by the given spectral data.

On determination of discontinuous Sturm-Liouville operator fromWeyl function

“…Differently from other studies, considered problem contains both the discontinuous coefficient r(x) and the discontinuity conditions at x = ξ ∈ (0, π). In the special cases, i.e., as c = 1, the inverse problems for Sturm-Liouville operator with discontinuous coefficient by Weyl function are examined in [1,4,11] and as r(x) ≡ 1, the inverse problems for Sturm-Liouville operator with discontinuity conditions by Weyl function are investigated in [6,7]. Moreover, the various works on the inverse problems for the discontinuous Sturm-Liouville operators can be given as follows: [3,5,9,10,[12][13][14][15][16][17][18] and the references therein.…”