A discontinuous Sturm–Liouville problem with boundary conditions rationally dependent on the eigenparameter

Abstract

Abstract The present paper deals with a class of discontinuous Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. Operator formulation is built and asymptotic formulas for eigenvalues and eigenfunctions are given. Moreover, the completeness of its eigenfunctions is also discussed.

Keywords

• Sturm–Liouville problem
• Eigenparameter dependent boundary condition
• Transmission condition
• Asymptotic formulae of eigenvalue and eigenfunction
• Completeness