TY - JOUR

T1 - A note on disconjugacy for second order systems

AU - Smith, Hal

PY - 1980/8

Y1 - 1980/8

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.

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U2 - 10.2140/pjm.1980.89.447

DO - 10.2140/pjm.1980.89.447

M3 - Article

AN - SCOPUS:84972520525

SN - 0030-8730

VL - 89

SP - 447

EP - 452

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -