THE ASYMPTOTIC-DISTRIBUTION OF THE EIGENVALUES OF RIGHT DEFINITE MULTIPARAMETER STURM-LIOUVILLE SYSTEMS

This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm-Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm-Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a ''multi-index'' oscillation number.