Eigenvalues of fourth-order differential operators with eigenparameter dependent boundary conditions

Abstract

This paper is concerned with a fourth-order differential operator with eigenparameter dependent boundary conditions. We prove that each of the eigenvalues of the problem can be embedded in a continuous eigenvalue branch. Furthermore, the differential expressions of the eigenvalues with respect to each of parameters are given.

Keywords

• fourth-order differential operator
• eigenparameter-dependent boundary condition
• dependence of eigenvalue
• differential expression