Oscillatory and spectral analysis of higher-order differential operators

Abstract

In the paper there are investigated the oscillatory properties of a 2nth order differential equation and the spectral properties of a 2nth order differential operator. These properties are established using the variational method, which relies on verifying a specific nth order differential inequality. Here, the coefficients of both the equation and the operator are the weights in this inequality. Furthermore, the characterization of the inequality occurs when the weights satisfy conditions, ensuring the existence of a certain combination of boundary values at infinity and at zero for the function involved in this inequality.