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An application of Lyapunov's direct method to the study of oscillations of a delay differential equation of even order

Part of: Qualitative theory

Published online by Cambridge University Press:  09 April 2009

Raymond D. Terry
Raymond D. Terry
Affiliation:
California Polytechnic State UniversitySan Luis Obispo, California 93407U.S.A.
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Abstract

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The direct method of Lyapunov is utilized to obtain a variety of criteria for the nonexistence of certain types of positive solutions of a delay differential equation of even order. Previous results of Terry (Pacific J. Math. 52 (1974), 269–282) are seen to be corollaries of the more general results of this paper.

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34C15: Nonlinear oscillations, coupled oscillators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 201 - 209
Copyright
Copyright © Australian Mathematical Society 1978

References

REFERENCES

Kiguradze, I. T. (1962), “Oscillation properties of solutions of certain ordinary differential equations”, Dokl. Akad. Nauk SSSR 144, 33–36; translated in Soviet Math. Dokl. 3 (1962), 649–652.Google Scholar
Terry, R. D. (1973), “Oscillatory properties of a fourth-order delay differential equation, 2”, Funkcial Ekvac. 16, 213–224.Google Scholar
Terry, R. D. (1974), “Oscillatory properties of a delay differential equation of even order”, Pacific J. Math. 52, 269–282.CrossRefGoogle Scholar
Terry, R. D. (1975), “Some oscillation criteria for delay differential equations of even order”, SIAM J. Appl. Math. 28, 319–334.CrossRefGoogle Scholar
Yoshizawa, T. (1970), “Oscillation property of solutions of second order differential equations”, Tohoku Math. J. 22, 619–634.CrossRefGoogle Scholar