Аннотация:
In the paper there are investigated the oscillatory properties of a 2nth order differential equation and the spectral properties of a 2nth order di erential operator. These properties are established using the variational method, which relies on verifying a speci c nth order differential inequality. Here, the coe cients 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 innity and at zero for the function involved in this inequality.
Ключевые слова и фразы:
higher-order differential equation, differential operator, oscillation, non-oscillation, spectrum, variational method, weighted inequality.
Полный текст:
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