On a Regular Sturm-Liouville Problem on a Finite Interval with the Eigenvalue Parameter Appearing Linearly in the Boundary Conditions

doi:10.1201/9780429332623-6

Chapter

On a Regular Sturm-Liouville Problem on a Finite Interval with the Eigenvalue Parameter Appearing Linearly in the Boundary Conditions

ABSTRACT

This work considers the eigenfunctions of a regular Sturm-Liouville problem on a finite interval with the eigenvalue parameter appearing linearly in the boundary conditions. It is shown that the eigenfunctions for this class of problems form a Riesz basis of the corresponding Hilbert space. A corresponding Rayleigh-Ritz formula is developed, and a lower bound estimation for eigenvalues is found.