ON LYAPUNOV TYPE FINITE DIFFERENCE INEQUALITY

Authors

  • B. G. PACHPATTE Department of Mathematics and Statistics, Marathwada University, Aurangabad 431004 (Maharashtra), INDIA.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4678

Keywords:

Lyapunov inequality, second order linear finite difference equation, distance between consecutive zeros

Abstract

Lyapunov type finite difference inequality is established which in the special case yields implicit lower bound on the distance between consecutive zeros of a nontrivial solution of a second order linear finite difference equation.

References

S. B. Eliason, "A Lyapunov inequality for a certain second order nonlinear differential equation", J. London Math. Soc. 2 (1970), 461-466.

A. M. Fink and D. F. St. Mary, "On an inequality of Nehari", Proc. Amer. Math. Soc. 21 (1969), 640-642.

P. Hartman, Ordinary Differential Equations, John Wiley and Sons, New York, 1964.

M. K. Kwong, "On Lyapunov's inequality for disfocality", J. Math. Anal. Appl. 83 (1981), 486-494.

A. M. Liapunov, Probleme generate de la stabilite du mouvement, Annals of Mathematices Study 17, Princeton University Press, 1949.

B. G. Pachpatte, "A note on Lyapunov type inequalities", Indian J. Pure Appl. Math., 21 (1990), 45-49.

W. T. Patula, "On the distance between zeros", Proc. Amer. Math. Soc. 52 (1975), 247-251.

W. T. Reid, "A generalized Liapunov inequality", J. Differential Equations 13 (1973), 182-196.

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Published

1990-12-01

How to Cite

PACHPATTE, B. G. (1990). ON LYAPUNOV TYPE FINITE DIFFERENCE INEQUALITY. Tamkang Journal of Mathematics, 21(4), 337-339. https://doi.org/10.5556/j.tkjm.21.1990.4678

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Papers