Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (1): 110-124.doi: 10.1016/S0252-9602(17)30120-0

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DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

Meiman SUN1, Guozheng YAN1,2   

  1. 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
    2. Hubei Key Laboratory of Mathematical Physics, Wuhan 430079, China
  • Received:2016-12-12 Online:2018-02-25 Published:2018-02-25
  • Contact: Guozheng YAN E-mail:yan_gz@mail.ccnu.edu.cn
  • 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.

Key words: exterior transmission eigenvalue, inverse scattering problem, Helmholtz equation

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