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Existence of nonoscillatory solutions of first order nonlinear neutral equations

Published online by Cambridge University Press:  17 February 2009

Lu Wudu
Lu Wudu
Affiliation:
Department of Mathematics, South China Normal University, Guangzhou, 510631, China.
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Abstract

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Consider the nonlinear neutral equation

where pi(t), hi(t), gj(t), Q(t) Є C[t0, ∞), limt→∞hi(t) = ∞, limt→∞gj(t) = ∞ i Є Im = {1, 2, …, m}, j Є In = {1, 2, …, n}. We obtain a necessary and sufficient condition (2) for this equation to have a nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorems 5 and 6) or to have a bounded nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorem 7).

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 2 , October 1990 , pp. 180 - 192
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Brayton, R. K., “Nonlinear oscillations in a distributed network”, Quart. Appl. Math. 24 (1967) 289–301.CrossRefGoogle Scholar
[2]Brayton, R. K. and Willoughby, R. A., “On the numerical integration of a symmetric system of difference-differential equations of neutral type”, J. Math. Appl. 18 (1967) 182–189.Google Scholar
[3]Grove, E. A., Kulenovic, M. R. S. and Ladas, G., “Sufficient conditions for oscillation and nonoscillation of neutral equations”, J. Differential Equations 68 (1987) 373–382.CrossRefGoogle Scholar
[4]Hale, J., Theory of functional differential equations (Springer-Verlag, New York, 1977).CrossRefGoogle Scholar