# Further higher monotonicity properties of Sturm-Liouville functions

Zuzana Došlá; Miloš Háčik; Martin E. Muldoon

Archivum Mathematicum (1993)

- Volume: 029, Issue: 1-2, page 83-96
- ISSN: 0044-8753

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topDošlá, Zuzana, Háčik, Miloš, and Muldoon, Martin E.. "Further higher monotonicity properties of Sturm-Liouville functions." Archivum Mathematicum 029.1-2 (1993): 83-96. <http://eudml.org/doc/247440>.

@article{Došlá1993,

abstract = {Suppose that the function $q(t)$ in the differential equation (1) $y^\{\prime \prime \}+q(t)y=0 $ is decreasing on $(b,\infty )$ where $b \ge 0$. We give conditions on $q$ which ensure that (1) has a pair of solutions $y_1(t),\;y_2(t)$ such that the $n$-th derivative ($n\ge 1$) of the function $p(t)= y_1^2(t) +y_2^2(t)$ has the sign $(- 1)^\{n+1\}$ for sufficiently large $t$ and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.},

author = {Došlá, Zuzana, Háčik, Miloš, Muldoon, Martin E.},

journal = {Archivum Mathematicum},

keywords = {n-times monotonic functions; completely monotonic functions; ultimately monotonic functions and sequences; regularly varying functions; Appell differential equation; generalized Airy equation; higher differences; ultimate monotonicity; regularly varying functions; higher monotonicity},

language = {eng},

number = {1-2},

pages = {83-96},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Further higher monotonicity properties of Sturm-Liouville functions},

url = {http://eudml.org/doc/247440},

volume = {029},

year = {1993},

}

TY - JOUR

AU - Došlá, Zuzana

AU - Háčik, Miloš

AU - Muldoon, Martin E.

TI - Further higher monotonicity properties of Sturm-Liouville functions

JO - Archivum Mathematicum

PY - 1993

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 029

IS - 1-2

SP - 83

EP - 96

AB - Suppose that the function $q(t)$ in the differential equation (1) $y^{\prime \prime }+q(t)y=0 $ is decreasing on $(b,\infty )$ where $b \ge 0$. We give conditions on $q$ which ensure that (1) has a pair of solutions $y_1(t),\;y_2(t)$ such that the $n$-th derivative ($n\ge 1$) of the function $p(t)= y_1^2(t) +y_2^2(t)$ has the sign $(- 1)^{n+1}$ for sufficiently large $t$ and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.

LA - eng

KW - n-times monotonic functions; completely monotonic functions; ultimately monotonic functions and sequences; regularly varying functions; Appell differential equation; generalized Airy equation; higher differences; ultimate monotonicity; regularly varying functions; higher monotonicity

UR - http://eudml.org/doc/247440

ER -

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