Abstract
The maximum and anti-maximum principles are extended to the case of eigenvalue Sturm–Liouville problemswith boundary conditions of Dirichlet type (if possible) on a bounded interval [a, b]. The function r is assumed to be continuous and > 0 on ]a, b[, but the function 1/r is not necessarily integrable on [a, b]. The conditions on the functions p, m and h depend on the integrability or nonintegrability of 1/r on [a, c] and/or [c, b], for some c ∈ ]a, b[. The weight function m is not necessarily of constant sign.
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