Some Eigenvalue Problems For Vectorial Sturm-Liouville Equations With Transmission Conditions

In this paper, the multiplicity of eigenvalues for a class of vectorial Sturm-Liouville equations with transmission conditions is considered. Firstly, a new inner product asso-ciated with the problems and a new space is constructed, we can see that the eigenvalues of the problems are real in this new space. Then we construct the fundamental solutions of the equation and show that A is an eigenvalue if and only if it’s a zero of the charac-teristic function ω(λ)=det[CΦ’(π:λ)+ Φ(π;λ)]. On this basis, we get the conclusion that the algebraic multiplicity of eigenvalues of the two-dimensional problems is equal to their geometric multiplicity.