Eigenvalues of fourth-order boundary value problems with distributional potentials

Abstract

This paper aims to investigate the fourth-order boundary value problems with distributional potentials. We first prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Then we obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problems: the boundary conditions, the coefficient functions and the endpoints. Moreover, we find the differential expressions for each parameter.

Keywords

• fourth-order boundary value problems
• distributional potentials
• quasi-derivatives
• eigenvalues