Sturm–Liouville problems are discussed under hypotheses too weak to guarantee uniqueness of solutions of the related initial value problems. The results include sharp upper and lower bounds for the nth characteristic value, a simple procedure for deducing existence of the nth characteristic function from its existence on subintervals for $n = 1$, a criterion for discreteness of the spectrum in a special case, and a brief proof of Sturm–s second comparison theorem. The methods are simpler than those sometimes used, and the results are more general than any previous results of this type known to me. However, the paper as a whole is expository.