Uniqueness Theorems for Inverse Problems of Discontinuous Sturm–Liouville Operator

On determination of discontinuous Sturm-Liouville operator fromWeyl function

“…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.…”

Relationship of the Green's functions related to the Hill's equation coupled to different boundary value conditions

“…has also been widely studied in the literature (see [1,3,7,9,11,13,[15][16][17][18][19][20] and the references therein), especially coupled to periodic conditions. In this sense, a particularly interesting case happens when σ has constant sign, which can be interpreted as the action of an external force acting over the system on a certain direction (positive or negative).…”