The Multiplicity of Eigenvalues of A Vectorial Singular Diffusion Equation with Discontinuous Conditions


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Ergün A.

Eastern Anatolian Journal of Science, cilt.6, sa.2, ss.22-34, 2020 (Hakemli Üniversite Dergisi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Konu: 2
  • Basım Tarihi: 2020
  • Dergi Adı: Eastern Anatolian Journal of Science
  • Sayfa Sayıları: ss.22-34

Özet

In this paper, we are studied m-dimensional

vectorial diffusion equation with jump conditions

inside a finite interval. We obtain some conclusions

about multiplicity of the eigenvalues based on the

estimation of solutions. Asymptotic formules of

eigenfunctions in each interval are obtained. Also,

properties related to the characteristic function of the

problem are given and proven. We prove that, under

certain conditions on potential matrix, the problem

can only have a finite number of eigenvalues with

multiplicity m.