Oscillation and spectral properties of some classes of higher order differential operators and weighted?nnth order differential inequalities

摘要

In this paper, we obtain strong oscillation and non-oscillation conditions fora class of higher order differential equations in dependence on an integral behaviorof its coefficients in a neighborhood of infinity. Moreover, we establish some spectralproperties of the corresponding higher order differential operator. In order to provethese we establish a certain weighted differential inequality of independent interest..