### 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) |
---|---|

Pages (from-to) | 447-452 |

Number of pages | 6 |

Journal | Pacific Journal of Mathematics |

Volume | 89 |

Issue number | 2 |

State | Published - 1980 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*89*(2), 447-452.

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

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 89, no. 2, pp. 447-452.

}

TY - JOUR

T1 - A note on disconjugacy for second order systems

AU - Smith, Hal

PY - 1980

Y1 - 1980

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972520525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972520525&partnerID=8YFLogxK

M3 - Article

VL - 89

SP - 447

EP - 452

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -