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

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Ergün A.

Eastern Anatolian Journal of Science, vol.6, no.2, pp.22-34, 2020 (International Refereed University Journal)

  • Publication Type: Article / Article
  • Volume: 6 Issue: 2
  • Publication Date: 2020
  • Title of Journal : Eastern Anatolian Journal of Science
  • Page Numbers: pp.22-34


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.