## Rocky Mountain Journal of Mathematics

### Existence of Positive Solutions of Higher Order Nonlinear Neutral Differential Equations

Satoshi Tanaka

#### Article information

Source
Rocky Mountain J. Math., Volume 30, Number 3 (2000), 1139-1149.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181070313

Digital Object Identifier
doi:10.1216/rmjm/1021477264

Mathematical Reviews number (MathSciNet)
MR1797835

Zentralblatt MATH identifier
0984.34068

#### Citation

Tanaka, Satoshi. Existence of Positive Solutions of Higher Order Nonlinear Neutral Differential Equations. Rocky Mountain J. Math. 30 (2000), no. 3, 1139--1149. doi:10.1216/rmjm/1021477264. https://projecteuclid.org/euclid.rmjm/1181070313

#### References

• Y. Chen, Existence of nonoscillatory solutions of $n$th order neutral delay differential equations, Funkcial. Ekvac. 35 (1992), 557-570.
• Q. Chuanxi and G. Ladas, Oscillations of higher order neutral differential equations with variable coefficients, Math. Nachr. 150 (1992), 15-24.
• L.H. Erbe, Q. Kong and B.G. Zhang, Oscillation theory for functional-differential equations, Marcel Dekker, Inc., New York, 1995.
• J.R. Graef and P.W. Spikes, On the oscillation of an nth-order nonlinear neutral delay differential equation, J. Comput. Appl. Math. 41 (1992), 35-40.
• M.K. Grammatikopoulos, G. Ladas and A. Meimaridou, Oscillation and asymptotic behavior of higher order neutral equations with variable coefficients, Chin. Ann. Math. Ser. B 9 (1988), 322-338.
• L. Györi and G. Ladas, Oscillation theory of delay differential equations, Oxford University Press, Oxford, 1991.
• J.K. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977.
• J. Jaroš and T. Kusano, Oscillation theory of higher order linear functional differential equations of neutral type, Hiroshima Math. J. 18 (1988), 509-531.
• --------, Asymptotic behavior of nonoscillatory solutions of nonlinear functional differential equations of neutral type, Funkcial. Ekvac. 32 (1989), 251-263.
• 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.
• M. Naito, An asymptotic theorem for a class of nonlinear neutral differential equations, Czechoslovak Math. J. 48 (1998), 419-432.
• Y. Naito, Nonoscillatory solutions of neutral differential equations, Hiroshima Math. J. 20 (1990), 231-258.
• --------, Asymptotic behavior of decaying nonoscillatory solutions of neutral differential equations, Funkcial. Ekvac. 35 (1992), 95-110.
• --------, Existence and asymptotic behavior of positive solutions of neutral differential equations, J. Math. Anal. Appl. 188 (1994), 227-244.
• --------, A note on the existence of nonoscillatory solutions of neutral differential equations, Hiroshima Math. J. 25 (1995), 513-518.
• S. Tanaka, Existence of positive solutions for a class of first-order neutral functional differential equations, J. Math. Anal. Appl. 229 (1999), 501-518.
• --------, Existence and asymptotic behavior of solutions of nonlinear neutral differential equations, in preparation.
• A. Zafer, Oscillation criteria for even order neutral differential equations, Appl. Math. Lett. 11 (1998), 21-25.
• B.G. Zhang and B. Yang, New approach of studying the oscillation of neutral differential equations, Funkcial. Ekvac. 41 (1998), 79-89.
• B.G. Zhang and J.S. Yu, On the existence of asymptotically decaying positive solutions of second order neutral differential equations, J. Math. Anal. Appl. 166 (1992), 1-11.
• B.G. Zhang, J.S. Yu and Z.C. Wang, Oscillations of higher order neutral differential equations, Rocky Mountain J. Math. 25 (1995), 557-568.