Electronic Journal of Differential Equations Electron. J. Diff. Eqns., Vol. 2009(2009), No. 28, pp. 1-14.
Liapunov-type integral inequalities for certain higher-order differential equations
Saroj Panigrahi
Abstract: In this paper, we obtain Liapunov-type integral inequalities for certain nonlinear, nonhomogeneous differential equations of higher order with without any restriction on the zeros of their higher-order derivatives of the solutions by using elementary analysis. As an applications of our results, we show that oscillatory solutions of the equation converge to zero as
. Using these inequalities, it is also shown that
as
, where
and
is an increasing sequence of zeros of an oscillatory solution of
,
, provided that
,
and for all
. A criterion for disconjugacy of nonlinear homogeneous equation is obtained in an interval
.
Submitted October 19, 2008. Published February 5, 2009.
Math Subject Classifications: 34C10.
Key Words: Liapunov-type inequality; oscillatory solution; disconjugacy; higher order differential equations.
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| Saroj Panigrahi Department of Mathematics and Statistics University of Hyderabad, Hyderabad 500 046, India email: spsm@uohyd.ernet.in, panigrahi2008@gmail.com |
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