Zettl: A new proof of the inequalities among SturmLiouville eigenvalues

Abstract. We consider self-adjoint regular Sturm-Liouville problems with positive leading coefficients and weight functions. A new proof of the inequalities among the eigenvalues for separated boundary conditions and those for coupled boundary conditions established recently by three of the authors with M. S. P. Eastham is given. This new proof does not assume that any special case of the inequalities has been proven. 1991 Mathematics Subject Classification: Primary 34B24; Secondary 34L05, 34L15. Key words: self-adjoint regular Sturm-Liouville problems, separated and coupled boundary conditions, inequalities among eigenvalues. Consider a self-adjoint regular Sturm-Liouville problem (SLP) with a positive leading coefficient and a positive weight function, i.e., (0.1) (0.2) wher