Finite spectrum of fourth-order boundary value problems with boundary and transmission conditions dependent on the spectral parameter

Abstract

A kind of fourth-order boundary value problem with eigenparameter-dependent boundary and transmission conditions is investigated. By constructing the characteristic function, we prove that the problems consist of a finite number of eigenvalues. We obtain that the number of eigenvalues of the problems not only depend on the order of the equation but also depend on the partition of the domain interval, the boundary conditions, and the eigenparameter-dependent transmission conditions.

Keywords

• fourth-order boundary value problems
• boundary and transmission conditions with spectral parameter
• eigenvalues
• finite spectrum
• 34l99
• 34b05
• 47a75