Stieltjes Sturm–Liouville equations: Eigenvalue dependence on problem parameters

We examine properties of eigenvalues and solutions to a 2n-dimensional Stieltjes Sturm–Liouville eigenvalue problem. Existence and uniqueness of a solution has been established previously. An earlier paper considered the corresponding initial value problem and established conditions which guarantee that solutions depend continuously on the coefficients [L.E. Battle, Solution dependence on problem parameters for initial value problems associated with the Stieltjes Sturm–Liouville equations, Electron. J. Differential Equations 2005 (2) (2005) 1–18]. Here, we find conditions which guarantee that the eigenvalues and solutions depend continuously on the coefficients, endpoints, and boundary data. For a simplified two-dimensional problem, we find conditions which guarantee the eigenvalues to be differentiable functions of the problem data.