On the spectrum of a parameter-dependent Sturm-Liouville problem

We study the spectrum of a parameter dependent Sturm-Liouville problem by using the continued fractions, through which necessary and sufficient conditions for eigenvalues are obtained. From these conditions estimates for large eigenvalues depending on the parameter and an asymptotic result for the lowest eigenvalue will follow. Furthermore, the use of the theory of orthogonal polynomials provides upper and lower bounds for the eigenvalues given in terms of the zeros of particular sequences of polynomials