A note on disconjugacy for second order systems

Research output: Contribution to journalArticle

6 Citations (Scopus)

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
StatePublished - 1980

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Disconjugacy
Second-order Systems
Non-negative
Valid
Sufficient
If and only if
Generalise
Necessary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A note on disconjugacy for second order systems. / Smith, Hal.

In: Pacific Journal of Mathematics, Vol. 89, No. 2, 1980, p. 447-452.

Research output: Contribution to journalArticle

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