Remarks on a New Inverse Nodal Problem
Copyright policy )Remarks on a New Inverse Nodal Problem
The authors weaken the conditions and simplify the proof of a theorem of \textit{X. F. Yang} [A new inverse nodal problem, J. Differ. Equations (to appear)]. It is known that the usual nodal inverse problem developed by \textit{J. R. McLaughlin} [J. Differ. Equations, 73, No. 2, 354-362 (1988; Zbl 0652.34029)] is overdetermined. That makes possible to reduce the data sufficient to determine the potential of the Sturm-Liouville equation and the boundary conditions. The authors use the results of \textit{F. Gesztesy} and \textit{B. Simon} [Inverse spectral analysis with partial information on the potential, II, The case of discrete spectrum, Trans. Am. Math. Soc. 352, No. 6, 2765-2787 (2000)].
Sturm-Liouville theory, nodal length, Borg's theorem, Applied Mathematics, Inverse problems involving ordinary differential equations, nodal inverse problem, Sturm-Liouville problem, Analysis
Sturm-Liouville theory, nodal length, Borg's theorem, Applied Mathematics, Inverse problems involving ordinary differential equations, nodal inverse problem, Sturm-Liouville problem, Analysis
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