Some Traces For An Eigenvalue Problem With Three-Point Boundary Conditions

In this paper, the asymptotic estimations of initial value solution are obtained for an eigenvalue problem with three-point boundary conditions by use of the iterate method. And constructing an entire function ω(λ), the zeros of which arethe eigenvalue problem with three-point boundary conditions. This eigenvalue problem with three-point boundary conditions is divided into two essential kinds: reflection and refraction. Moreover, in different special cases the three-point boundary conditions are categorized into nine element types, thus nine corresponding entirefunctions ω(λ) deciding eigenvalue and their asymptotic estimations on thecorresponding circuits are gotten. By restorting to the integral identity and the residue method, asymptotic estimations of the eigenvalue problem are considered and eigenvalue's trace identities are obtained.