Oscillatory and nonoscillatory solutions of neutral differential equations

Satoshi Tanaka

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 2, page 169-184
  • ISSN: 0066-2216

Abstract

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Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.

How to cite

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Tanaka, Satoshi. "Oscillatory and nonoscillatory solutions of neutral differential equations." Annales Polonici Mathematici 73.2 (2000): 169-184. <http://eudml.org/doc/262556>.

@article{Tanaka2000,
abstract = {Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.},
author = {Tanaka, Satoshi},
journal = {Annales Polonici Mathematici},
keywords = {nonoscillatory solution; neutral differential equation; oscillatory solution; oscillatory and nonoscillatory solutions; existence},
language = {eng},
number = {2},
pages = {169-184},
title = {Oscillatory and nonoscillatory solutions of neutral differential equations},
url = {http://eudml.org/doc/262556},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Tanaka, Satoshi
TI - Oscillatory and nonoscillatory solutions of neutral differential equations
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 2
SP - 169
EP - 184
AB - Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.
LA - eng
KW - nonoscillatory solution; neutral differential equation; oscillatory solution; oscillatory and nonoscillatory solutions; existence
UR - http://eudml.org/doc/262556
ER -

References

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  1. [1] Y. Chen, Existence of nonoscillatory solutions of nth order neutral delay differential equations, Funkcial. Ekvac. 35 (1992), 557-570. Zbl0787.34056
  2. [2] L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 1995. Zbl0821.34067
  3. [3] I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Univer. Press, 1991. Zbl0780.34048
  4. [4] J. K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977. Zbl0352.34001
  5. [5] J. Jaroš, Y. Kitamura and T. Kusano, On a class of functional differential equations of neutral type, in: Recent Trends in Differential Equations, World Sci. Ser. Appl. Anal. 1, World Scientific, 1992, 317-333. Zbl0832.34067
  6. [6] J. Jaroš and T. Kusano, Oscillation theory of higher order linear functional differential equations of neutral type, Hiroshima Math. J. 18 (1988), 509-531. Zbl0693.34038
  7. [7] J. Jaroš and T. Kusano, Existence of oscillatory solutions for functional differential equations of neutral type, Acta Math. Univ. Comenian. 60 (1991), 185-194. Zbl0745.34067
  8. [8] Y. Kitamura and T. Kusano, Oscillation and asymptotic behavior of solutions of first-order functional differential equations of neutral type, Funkcial. Ekvac. 33 (1990), 325-343. Zbl0722.34064
  9. [9] Y. Kitamura and T. Kusano, Existence theorems for a neutral functional differential equation whose leading part contains a difference operator of higher degree, Hiroshima Math. J. 25 (1995), 53-82. Zbl0828.34054
  10. [10] Y. Kitamura, T. Kusano and B. S. Lalli, Existence of oscillatory and nonoscillatory solutions for a class of neutral functional differential equations, Math. Bohem. 120 (1995), 57-69. Zbl0838.34079
  11. [11] W. T. Li, Classifications and existence of nonoscillatory solutions of second order nonlinear neutral differential equations, Ann. Polon. Math. 65 (1997), 283-302. Zbl0873.34065
  12. [12] M. Naito, An asymptotic theorem for a class of nonlinear neutral differential equations, Czechoslovak Math. J. 48 (1998), 419-432. 
  13. [13] Y. Naito, Nonoscillatory solutions of neutral differential equations, Hiroshima Math. J. 20 (1990), 231-258. Zbl0721.34091
  14. [14] Y. Naito, Asymptotic behavior of decaying nonoscillatory solutions of neutral differential equations, Funkcial. Ekvac. 35 (1992), 95-110. Zbl0771.34054
  15. [15] S. Tanaka, Existence of positive solutions for a class of first-order neutral functional differential equations, J. Math. Anal. Appl. 229 (1999), 501-518. Zbl0920.34066

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