Estimates of complex eigenvalues and an inverse spectral problem for the transmission eigenvalue problem

Xu, Xiao-Chuan and Yang, Chuan-Fu and Buterin, Sergey A. and Yurko, Vjacheslav A.: Estimates of complex eigenvalues and an inverse spectral problem for the transmission eigenvalue problem. Electronic journal of qualitative theory of differential equations 38. pp. 1-15. (2019)

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Abstract

This work deals with the interior transmission eigenvalue problem: y 00 + k 2η (r) y = 0 with boundary conditions y (0) = 0 = y 0 (1) sin k k − y (1) cos k, where the function η(r) is positive. We obtain the asymptotic distribution of non-real transmission eigenvalues under the suitable assumption on the square of the index of refraction η(r). Moreover, we provide a uniqueness theorem for the case R 1 0 p η(r)dr > 1, by using all transmission eigenvalues (including their multiplicities) along with a partial information of η(r) on the subinterval. The relationship between the proportion of the needed transmission eigenvalues and the length of the subinterval on the given η(r) is also obtained.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 38
Page Range: pp. 1-15
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.38
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 13-15. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 27. 13:17
Last Modified: 2019. Sep. 27. 13:27
URI: http://acta.bibl.u-szeged.hu/id/eprint/62116

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