Linearized comparison criteria for a nonlinear neutral differential equation

Xinping Guan; Sui Sun Cheng

Annales Polonici Mathematici (1996)

  • Volume: 64, Issue: 2, page 161-173
  • ISSN: 0066-2216

Abstract

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A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.

How to cite

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Xinping Guan, and Sui Sun Cheng. "Linearized comparison criteria for a nonlinear neutral differential equation." Annales Polonici Mathematici 64.2 (1996): 161-173. <http://eudml.org/doc/269943>.

@article{XinpingGuan1996,
abstract = {A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.},
author = {Xinping Guan, Sui Sun Cheng},
journal = {Annales Polonici Mathematici},
keywords = {neutral differential equations; positive solutions; linearized comparison theorems; positive solution; nonlinear neutral differential equation},
language = {eng},
number = {2},
pages = {161-173},
title = {Linearized comparison criteria for a nonlinear neutral differential equation},
url = {http://eudml.org/doc/269943},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Xinping Guan
AU - Sui Sun Cheng
TI - Linearized comparison criteria for a nonlinear neutral differential equation
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 2
SP - 161
EP - 173
AB - A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.
LA - eng
KW - neutral differential equations; positive solutions; linearized comparison theorems; positive solution; nonlinear neutral differential equation
UR - http://eudml.org/doc/269943
ER -

References

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  3. [3] M. K. Grammatikopoulous, Y. G. Sficas and I. P. Stavroulakis, Necessary and sufficient conditions for oscillations of neutral equations with several coefficients, J. Differential Equations 76 (1988), 294-311. 
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  8. [8] W. Lu, Existence of nonoscillatory solutions of first order nonlinear neutral equations, J. Austral. Math. Soc. Ser. B 32 (1990), 180-192. Zbl0723.34069
  9. [9] W. Lu, Nonoscillation and oscillation for first order nonlinear equations, Funkcial. Ekvac. 37 (1994), 383-394. Zbl0808.34079
  10. [10] R. Olah, Oscillation of differential equation of neutral type, Hiroshima Math. J. 25 (1995), 1-10. Zbl0831.34076
  11. [11] C. Qian, G. Ladas, B. G. Zhang and T. Zhao, Sufficient conditions for oscillation and existence of positive solutions, Appl. Anal. 35 (1990), 187-194. Zbl0709.34055
  12. [12] J. H. Shen and Z. C. Wang, Oscillation and nonoscillation for a class of nonlinear neutral differential equations, Differential Equations Dynam. Systems 2 (1994), 347-360. Zbl0873.34057
  13. [13] J. Yan, Oscillation of solutions of first order delay differential equations, Nonlinear Anal. 11 (1987), 1279-1287. Zbl0639.34067
  14. [14] J. S. Yu and Z. Wang, A linearized oscillation result for neutral delay differential equations, Math. Nachr. 163 (1993), 101-107. Zbl0805.34065
  15. [15] B. G. Zhang and J. S. Yu, Oscillation and nonoscillation for neutral differential equations, J. Math. Anal. Appl. 172 (1993), 11-23. Zbl0776.34059

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