On n th order differential equations over Hardy fields

A. Ramayyan

Kybernetika (1994)

  • Volume: 30, Issue: 4, page 461-470
  • ISSN: 0023-5954

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Ramayyan, A.. "On $n$th order differential equations over Hardy fields." Kybernetika 30.4 (1994): 461-470. <http://eudml.org/doc/27311>.

@article{Ramayyan1994,
author = {Ramayyan, A.},
journal = {Kybernetika},
keywords = {linear ordinary differential equation; Hardy field; nonhomogeneous th order; nonoscillatory},
language = {eng},
number = {4},
pages = {461-470},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On $n$th order differential equations over Hardy fields},
url = {http://eudml.org/doc/27311},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Ramayyan, A.
TI - On $n$th order differential equations over Hardy fields
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 4
SP - 461
EP - 470
LA - eng
KW - linear ordinary differential equation; Hardy field; nonhomogeneous th order; nonoscillatory
UR - http://eudml.org/doc/27311
ER -

References

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  1. M. Boshernitzan, An extension of Hardy's class of orders of infinity, J. Analyse Math. 39 (1981), 235-255. (1981) MR0632463
  2. M. Boshernitzan, New orders of finity, J. Analyse Math. 41 (1982), 130-167. (1982) MR0687948
  3. M. Boshernitzan, Second order differential equations over Hardy fields, J. London Math. Soc. 35 (1987), 2, 109-120. (1987) Zbl0616.26002MR0871769
  4. M. Boshernitzan, Orders of infinity generated by difference equations, Amer. J. Math. 106 (1984), 1067-1089. (1984) Zbl0602.26002MR0761579
  5. M. Boshernitzan, Hardy fields and existence of trans exponential functions, Acquationes Math. 30 (1986), 258-280. (1986) MR0843667
  6. E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall of India Private Ltd., New Delhi 1974. (1974) MR0126573
  7. G. H. Hardy, Orders of Infinity, Cambridge University Press, London 1954. (1954) 
  8. A. R. Forsyth, A Treatise on Differential Equations, Sixth edition. Mac Millan and Co. Ltd., New York 1954. (1954) 
  9. V. Maric, Asymptotic behaviour of solutions of a nonlinear differential equation of the first order, J. Math. Anal. Appl. 38 (1972), 187-192. (1972) MR0306640
  10. M. Rosenlicht, Hardy fields, J. Math. Anal. Appl. 93 (1983), 297-311. (1983) Zbl0518.12014MR0700146
  11. M. Rosenlicht, The rank of a Hardy field, Trans. Amer. Math. Soc. 280 (1983), 659-671. (1983) Zbl0536.12015MR0716843
  12. M. Rosenlicht, Rank change on adjoint real powers to Hardy fields, Trans. Amer. Math. Soc. 284 (1984), 829-836. (1984) MR0743747
  13. M. Rosenlicht, Growth properties of functions in Hardy fields, Trans. Amer. Math. Soc. 299 (1987), 261-272. (1987) Zbl0619.34057MR0869411
  14. M. Rosenlicht, Asymptotic solutions of y ' ' = F ( x ) y , (Unpublished.) Zbl0824.34068

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