Articles

DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

  • Meiman SUN ,
  • Guozheng YAN
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  • 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
    2. Hubei Key Laboratory of Mathematical Physics, Wuhan 430079, China

Received date: 2016-12-12

  Online published: 2018-02-25

Supported by

This research is supported by National Natural Science Foundation of People's Republic of China (11571132 and 11171127), and Supported in Part by Program for Changjiang Scholars and Innovative Research Team in University No.IRT13066.

Abstract

In this paper we consider a kind of exterior transmission problem in which the refractive index n(x) is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.

Cite this article

Meiman SUN , Guozheng YAN . DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES[J]. Acta mathematica scientia, Series B, 2018 , 38(1) : 110 -124 . DOI: 10.1016/S0252-9602(17)30120-0

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