Electron. J. Differential Equations, Vol. 2017 (2017), No. 226, pp. 1-11.

Uniqueness theorems for Sturm-Liouville operators with interior twin-dense nodal set

Yu Ping Wang

We study Inverse problems for the Sturm-Liouville operator with Robin boundary conditions. We establish two uniqueness theorems from the twin-dense nodal subset $W_{S}([\frac{1-\varepsilon}{2},\frac{1}{2}])$, $ 0<\varepsilon\leq1$, together with parts of either one spectrum, or the minimal nodal subset $\{x_n^1\}_{n=1}^\infty$ on the interval [0,1/2]. In particular, if one spectrum is given a priori, then the potential q on the whole interval [0,1] can be uniquely determined by $W_{S}([\frac{1-\varepsilon}{2},\frac{1}{2}])$ for any S and arbitrarily small $\varepsilon$.

Submitted September 19, 2016. Published September 20, 2017.
Math Subject Classifications: 34A55, 34B24, 47E05.
Key Words: Uniqueness theorem; inverse nodal problem; potential; Sturm-Liouville operator; the interior twin-dense nodal subset.

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Yu Ping Wang
Department of Applied Mathematics
Nanjing Forestry University
Nanjing, Jiangsu 210037, China
email: ypwang@njfu.com.cn

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