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A Lyapunov inequality and forced oscillations in general nonlinear nth order differential-difference equations†

Published online by Cambridge University Press:  18 May 2009

Lu-San Chen
Lu-San Chen
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan
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The purpose of this paper is to consider the general nonlinear nth order differential-difference equation

and derive an inequality of Lyapunov type. Later we use this inequality to find conditions to ensure that the oscillatory solutions of equation (1) tend to zero as t → ∞. The conditions that ensure that the oscillatory solutions of equation (1) tend to zero, also cause all solutions of equation

to be non-oscillatory.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 161 - 166
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Hartman, P., Ordinary differential equations (Wiley, 1964), 345–346, 401.Google Scholar
2.Eliason, S. B., A Lyapunov inequality for a certain second order nonlinear differential equation, J. London Math. Soc. (2) 2 (1970), 461–466.CrossRefGoogle Scholar
3.Bradley, J. S., Oscillation theorems for a second order delay equation, J. Differential Equations 8 (1970), 397–403.CrossRefGoogle Scholar
4.Dahiya, R. S. and Singh, B., A Lyapunov inequality and nonoscillation theorem for a second order nonlinear differential-difference equation, J. Mathematical and Physical Sci. 7 (1973), 163–170.Google Scholar
5.Singh, B., Forced oscillations in general ordinary differential equations, Tamkang J. Math. 6 (1975), 5–11.Google Scholar
6.Hammelt, M. E., Nonoscillation properties of a nonlinear differential equation, Proc. Amer. Math. Soc. 30 (1971), 92–96.CrossRefGoogle Scholar
7.Londen, S., Some nonoscillation theorems for a second order nonlinear differential equation, SIAM J. Math. Anal. 4 (1973), 460–465.CrossRefGoogle Scholar