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
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