A note on disconjugacy for second order systems

Hal Smith

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

It is well-known that the equationis disconjugate on [a, b] if and only if there exists a solutionwhich is positive on [a, 6], in the case that A(t) is scalarvalued.In this note we generalize this simple result to thecase where A(t)=((aij(t)) is an nxn matrix-valued functionwhich satisfies certain generalized sign conditions. Theseresults apply, for instance, if the off diagonal elementsare nonnegative. Simple necessary and sufficient conditionsare given for disconjugacy if A(t) = A and these are usedto construct examples showing the necessity of sign conditionson A(t) for the above mentioned results and other results of Sturm type for systems to be valid.

Original languageEnglish (US)
Pages (from-to)447-452
Number of pages6
JournalPacific Journal of Mathematics
Volume89
Issue number2
DOIs
StatePublished - Aug 1980

ASJC Scopus subject areas

  • Mathematics(all)

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