Dispersions for linear differential equations of arbitrary order

František Neuman

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 1-2, page 147-155
  • ISSN: 0044-8753

Abstract

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For linear differential equations of the second order in the Jacobi form y ' ' + p ( x ) y = 0 O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated.

How to cite

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Neuman, František. "Dispersions for linear differential equations of arbitrary order." Archivum Mathematicum 033.1-2 (1997): 147-155. <http://eudml.org/doc/248029>.

@article{Neuman1997,
abstract = {For linear differential equations of the second order in the Jacobi form \[ y^\{\prime \prime \} + p(x)y = 0 \] O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated.},
author = {Neuman, František},
journal = {Archivum Mathematicum},
keywords = {linear differential equations; distribution of zeros; asymptotic behaviour; Abel’s functional equation; linear differential equations; distribution of zeros; asymptotic behaviour; Abel's functional equation},
language = {eng},
number = {1-2},
pages = {147-155},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Dispersions for linear differential equations of arbitrary order},
url = {http://eudml.org/doc/248029},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Neuman, František
TI - Dispersions for linear differential equations of arbitrary order
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 1-2
SP - 147
EP - 155
AB - For linear differential equations of the second order in the Jacobi form \[ y^{\prime \prime } + p(x)y = 0 \] O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated.
LA - eng
KW - linear differential equations; distribution of zeros; asymptotic behaviour; Abel’s functional equation; linear differential equations; distribution of zeros; asymptotic behaviour; Abel's functional equation
UR - http://eudml.org/doc/248029
ER -

References

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  1. O rozložení nulových bodů řešení lineární diferenciální rovnice y ' ' = Q ( t ) y a jejich derivací, Acta F. R. N. Univ. Comenian 5 (1961), 465–474. (1961) 
  2. Linear Differential Transformations of the Second Order, The English Univ. Press, London, 1971. (1971) MR0463539
  3. On differentiable solutions of a functional equation, Ann. Polon. Math. 13 (1963), 133–138. (1963) MR0153998
  4. Functional Equations in a Single Variable, PWN, Warszawa, 1968. (1968) Zbl0196.16403MR0228862
  5. Distribution of zeros of solutions of y ' ' = q ( t ) y in relation to their behaviour in large, Studia Sci. Math. Hungar 8 (1973), 177–185. (1973) Zbl0286.34050MR0333344
  6. Global Properties of Linear Ordinary Differential Equations, Mathematics and Its Applications (East European Series) 52, Kluwer Acad. Publ., Dordrecht-Boston-London, 1991, ISBN 0-7923-1269-4. (1991, ISBN 0-7923-1269-4) MR1192133

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