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In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.

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We present new interval oscillation criteria related to integral averaging technique for certain classes of second-order nonlinear differential equations which are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t 0 , ∞), rather than on the whole half-line. They generalize and improve some known results. Examples are also given to illustrate the importance of our results.  2004 Elsevier Inc. All rights reserved.

Some new oscillation criteria are given for general nonlinear second-order ordinary differential equations with damping of the form x′′ + p ( t ) x′ + q ( t ) f ( x ) = 0, where f is monotone or nonmonotone. Our results generalize and extend some earlier results of Deng.

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