A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions
2012 ◽
Vol 43
(1)
◽
pp. 145-152
◽
Keyword(s):
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 $\alpha\in [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $\frac{a_2\lambda+b_2}{c_2\lambda+d_2}$ of the boundary condition are uniquely determined by a subset $S\subset \sigma (L)$ and fractional linear function $\frac{a_1\lambda+b_1}{c_1\lambda+d_1}$ of the boundary condition.
2012 ◽
Vol 43
(2)
◽
pp. 289-299
◽
2016 ◽
Vol 24
(4)
◽
2012 ◽
Vol 36
(7)
◽
pp. 857-868
◽
Keyword(s):
2018 ◽
Vol 69
(9)
◽
pp. 1416-1423
◽
2016 ◽
Vol 24
(3)
◽
2019 ◽
Vol 50
(3)
◽
pp. 207-221
◽
2017 ◽
Keyword(s):