Abstract
AbstractThe Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.
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