Lower bounds for eigenvalues of Sturm-Liouville problems with discontinuous coefficients: integral equation methods

Abstract

This paper is concerned with application of the theory of Fredholm integral equations to Sturm-Liouville problems with discontinuous coefficients. Such problems occur naturally in many areas of application involving mechanics of heterogeneous media. Due to the nonsmoothness of the coefficients, the eigenvalue spectrum may exhibit severe irregularities. Lower bounds for eigenvalues are obtained which reflect this behavior. Numerical results are presented for example problems previously treated using other methods.