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The inverse nodal problem and the Ambarzumyan problem for the p-Laplacian

Published online by Cambridge University Press:  04 November 2009

C. K. Law ,
Wei-Cheng Lian  and
Wei-Chuan Wang
C. K. Law
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, and National Center for Theoretical Sciences, Taiwan, (law@math.nsysu.edu.tw)
Wei-Cheng Lian
Affiliation:
Department of Information Management, National Kaohsiung Marine University, Kaohsiung 811, Taiwan, (wclian@mail.nkmu.edu.tw)
Wei-Chuan Wang
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, and National Center for Theoretical Sciences, Taiwan, (wangwc@math.nsysu.edu.tw)
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Abstract

We study the issues of the reconstruction and stability of the inverse nodal problem for the one-dimensional p-Laplacian eigenvalue problem. A key step is the application of a modified Prüfer substitution to derive a detailed asymptotic expansion for the eigenvalues and nodal lengths. Two associated Ambarzumyan problems are also solved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 6 , December 2009 , pp. 1261 - 1273
Copyright
Copyright © Royal Society of Edinburgh 2009

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