### 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)=((a_{ij}(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 language | English (US) |
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Pages (from-to) | 447-452 |

Number of pages | 6 |

Journal | Pacific Journal of Mathematics |

Volume | 89 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1980 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Smith, H. (1980). A note on disconjugacy for second order systems.

*Pacific Journal of Mathematics*,*89*(2), 447-452. https://doi.org/10.2140/pjm.1980.89.447