Continuous dependence of the transmission eigenvalues in one dimension

Yalin Zhang; Guoliang Shi

doi:10.3934/ipi.2015.9.273

Article Contents

2015, Volume 9, Issue 1: 273-287. Doi: 10.3934/ipi.2015.9.273

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Continuous dependence of the transmission eigenvalues in one dimension

Yalin Zhang^1, and
Guoliang Shi^1,

1.
Department of Mathematics, Tianjin University, Tianjin, 300072

Received: May 2014

Revised: September 2014

Published: February 2015

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Abstract

The transmission eigenvalue problem on the interval $\left[ a,b\right] $ is considered. We show that the isolated transmission eigenvalues are continuous functions of the coefficients of the problem and that the transmission eigenfunctions can be normalized so that they depend continuously on all coefficients in the uniform norm. Throughout this work, our results are established without assumptions on the sign of the contrasts.

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Mathematics Subject Classification: Primary: 34B40, 34L25; Secondary: 78A25.

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