Sturm-Liouville Problems with Several Parameters.

We consider the regular linear Sturm-Liouville problem second-order linear ordinary differential equation with boundary conditions at two points x 0 and x 1, those conditions being separated and homogeneous with several real parameters lambda 1, lambda N. Solutions to those problems correspond to eigenvalues lambda lambda 1, lambda N lying on surfaces in R superscript N determined by the number of zeroes in 0,1 of solutions. We describe properties of these surfaces, including boundedness, and when unbounded, asymptotic directions. Using these properties some results are given for the system of N Sturm-Liouville problems which share only the parameters. Sharp results are given for the system of two problems sharing two parameters.