Open AccessA unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions
Author(s) -
Yuping Wang
Publication year - 2012
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.43.2012.1024
Subject(s) - mathematics , lambda , uniqueness , interval (graph theory) , boundary value problem , function (biology) , uniqueness theorem for poisson's equation , boundary (topology) , inverse , sturm–liouville theory , mathematical analysis , combinatorics , geometry , physics , quantum mechanics , evolutionary biology , biology
In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on $[0,frac{1}{2}+alpha]$ for some $alphain [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $frac{a_2lambda+b_2}{c_2lambda+d_2}$ of the boundary condition are uniquely determined by a subset $Ssubset sigma (L)$ and fractional linear function $frac{a_1lambda+b_1}{c_1lambda+d_1}$ of the boundary condition