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On Some New Inverse nodal problems

by Cheng, Yan-Hsiou

Abstract (Summary)
In this thesis, we study two new inverse nodal problems introduced by Yang, Shen and Shieh respectively. Consider the classical Sturm-Liouville problem: $$ left{ egin{array}{c} -phi'+q(x)phi=la phi phi(0)cosalpha+phi'(0)sinalpha=0 phi(1)coseta+phi'(1)sineta=0 end{array} ight. , $$ where $qin L^1(0,1)$ and $al,ein [0,pi)$. The inverse nodal problem involves the determination of the parameters $(q,al,e)$ in the problem by the knowledge of the nodal points in $(0,1)$. In 1999, X.F. Yang got a uniqueness result which only requires the knowledge of a certain subset of the nodal set. In short, he proved that the set of all nodal points just in the interval $(0,b) (frac{1}{2}Bibliographical Information:

Advisor:Tzon-Tzer Lu; Hua-Huai Chern; Tzy-Wei Hwang; Jhishen Tsay; Chun-Kong Law

School:National Sun Yat-Sen University

School Location:China - Taiwan

Source Type:Master's Thesis

Keywords:sturm liouville nodal set inverse problem

ISBN:

Date of Publication:07/17/2000

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