Oscillatory and asymptotic behaviour of solutions of advanced functional equations

Jozef Džurina

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 3-4, page 161-166
  • ISSN: 0044-8753

Abstract

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In this paper we compare the asymptotic behaviour of the advanced functional equation L n u ( t ) - F ( t , u [ g ( t ) ] ) = 0 with the asymptotic behaviour of the set of ordinary functional equations α i u ( t ) - F ( t , u ( t ) ) = 0 . On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.

How to cite

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Džurina, Jozef. "Oscillatory and asymptotic behaviour of solutions of advanced functional equations." Archivum Mathematicum 029.3-4 (1993): 161-166. <http://eudml.org/doc/247450>.

@article{Džurina1993,
abstract = {In this paper we compare the asymptotic behaviour of the advanced functional equation \[ L\_nu(t)-F\big (t,u[g(t)]\big )= 0\] with the asymptotic behaviour of the set of ordinary functional equations \[ \alpha \_iu(t)-F\big (t,u(t)\big )= 0. \] On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.},
author = {Džurina, Jozef},
journal = {Archivum Mathematicum},
keywords = {comparison theorem; advanced argument; property (B); oscillation; comparison theorem; asymptotic behaviour; advanced functional equation},
language = {eng},
number = {3-4},
pages = {161-166},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillatory and asymptotic behaviour of solutions of advanced functional equations},
url = {http://eudml.org/doc/247450},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Džurina, Jozef
TI - Oscillatory and asymptotic behaviour of solutions of advanced functional equations
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 3-4
SP - 161
EP - 166
AB - In this paper we compare the asymptotic behaviour of the advanced functional equation \[ L_nu(t)-F\big (t,u[g(t)]\big )= 0\] with the asymptotic behaviour of the set of ordinary functional equations \[ \alpha _iu(t)-F\big (t,u(t)\big )= 0. \] On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.
LA - eng
KW - comparison theorem; advanced argument; property (B); oscillation; comparison theorem; asymptotic behaviour; advanced functional equation
UR - http://eudml.org/doc/247450
ER -

References

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  1. Nonoscillatory solutions of higher order differential equations, J. Math. Anal. Appl. 71 (1979), 1-17. (1979) MR0545858
  2. Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234-258. (1948) Zbl0031.35402MR0027925
  3. On the oscillation of solutions of the equation d m u / d t m + a ( t ) | u | n s i g n u = 0 , Mat. Sb. 65 (1964), 172-187. (Russian) (1964) Zbl0135.14302MR0173060
  4. Comparison theorems for functional differential equations with deviating arguments, J. Math. Soc. Japan 3 (1981), 509-532. (1981) MR0620288
  5. Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations, Proc. Roy. Soc. Edinburg 90 (1981), 25-40. (1981) MR0636062
  6. Canonicals form and principal systems for general disconjugate equations, Trans. Amer. Math. Soc. 189 (1974), 319-327. (1974) MR0330632

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