ON THE SPECTRUM OF A PARAMETER-DEPENDENT STURM-LIOUVILLE PROBLEM

Abstract

We study the spectrum of a parameter-dependent Sturm-Liouville problem. By using, as the main tool, the theory of continued fractions we obtain a characterization of the eigenvalues. From here estimates for large eigenvalues, depending on the parameter, and an asymptotic result for the lowest eigenvalue will follow. We associate to each given eigenvalue two sequences converging monotonically to the eigenvalue itself, one from above and the other from below. To obtain this result we use the theory of orthogonal polynomials.