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

Abstract

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.

Keywords

• Vectorial Diffusion problem
• Multiplicity eigenvalues
• Jump conditions.

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