ON LYAPUNOV TYPE FINITE DIFFERENCE INEQUALITY
Keywords:Lyapunov inequality, second order linear finite difference equation, distance between consecutive zeros
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.
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.
How to Cite
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.