Comparison theorems for functional differential equations

Jozef Džurina

Mathematica Bohemica (1994)

  • Volume: 119, Issue: 2, page 203-211
  • ISSN: 0862-7959

Abstract

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In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation L n u ( t ) + p ( t ) f ( u [ g ( t ) ] ) = 0 are compared with those of the functional differential equation α n u ( t ) + q ( t ) h ( u [ w ( t ) ] ) = 0 .

How to cite

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Džurina, Jozef. "Comparison theorems for functional differential equations." Mathematica Bohemica 119.2 (1994): 203-211. <http://eudml.org/doc/29231>.

@article{Džurina1994,
abstract = {In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation $L_nu(t)+p(t)f(u[g(t)])=0$ are compared with those of the functional differential equation $\alpha _nu(t)+q(t)h(u[w(t)])=0$.},
author = {Džurina, Jozef},
journal = {Mathematica Bohemica},
keywords = {functional differential equation; oscillatory; nonoscillatory; canonical form; property (A); functional differential equation; oscillatory; nonoscillatory; canonical form; property (A)},
language = {eng},
number = {2},
pages = {203-211},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Comparison theorems for functional differential equations},
url = {http://eudml.org/doc/29231},
volume = {119},
year = {1994},
}

TY - JOUR
AU - Džurina, Jozef
TI - Comparison theorems for functional differential equations
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 2
SP - 203
EP - 211
AB - In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation $L_nu(t)+p(t)f(u[g(t)])=0$ are compared with those of the functional differential equation $\alpha _nu(t)+q(t)h(u[w(t)])=0$.
LA - eng
KW - functional differential equation; oscillatory; nonoscillatory; canonical form; property (A); functional differential equation; oscillatory; nonoscillatory; canonical form; property (A)
UR - http://eudml.org/doc/29231
ER -

References

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  1. J. Džurinа, Oscillation and asymptotic properties of n-th order differential equations, Czech. Math. J. 42 (1992), 11-14. (1992) MR1152163
  2. J. Džurinа, Comparison theorems for nonlinear ODEs, Math. Slovaca 42 (1992), 299-315. (1992) MR1182960
  3. L. Erbe, 10.4153/CMB-1973-011-1, Canad. Math. Bull. 16 (1973), 49-56. (1973) MR0324173DOI10.4153/CMB-1973-011-1
  4. L. Erbe, 10.1137/0507040, SIAM Ј. Math. Anal. 7 (1976), 491-500. (1976) Zbl0356.34086MR0433001DOI10.1137/0507040
  5. E. Hille, 10.1090/S0002-9947-1948-0027925-7, Trans. Amer. Math. Soc. 64 (1948), 234-258. (1948) Zbl0031.35402MR0027925DOI10.1090/S0002-9947-1948-0027925-7
  6. I. T. Kigurаdze, 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. (In Russian.) (1964) 
  7. T. Kusаno аnd M. Nаito, Comparison theorems for functional differential equations with deviating arguments, Ј. Math. Soc. Јapan 3 (1981), 509-532. (1981) MR0620288
  8. T. Kusаno аnd M. Nаito, 10.2140/pjm.1981.92.345, Pacific Ј. Math. 92 (1981), 345-355. (1981) MR0618070DOI10.2140/pjm.1981.92.345
  9. W. E. Mаhfoud, 10.2140/pjm.1979.83.187, Pacifìc Ј. Math. 83 (1979), 187-197. (1979) MR0555047DOI10.2140/pjm.1979.83.187
  10. W. F. Trench, 10.1090/S0002-9947-1974-0330632-X, Trans. Amer. Math. Soc. 189 (1974), 319-327. (1974) Zbl0289.34051MR0330632DOI10.1090/S0002-9947-1974-0330632-X
  11. W. F. Trench, 10.1090/S0002-9939-1975-0379987-7, Proc. Amer. Math. Soc. 52 (1975), 147-155. (1975) Zbl0321.34027MR0379987DOI10.1090/S0002-9939-1975-0379987-7

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