On oscillatory and spectral properties of a class of higher-order differential operators

Aigerim Aisultankyzy Kalybay, Ryskul Oinarovich Oinarov

2023

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DOI 10.21203/rs.3.rs-3640654/v1
Data confidence 70 medium
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Abstract

Abstract In the paper, we study the oscillatory properties of a 2nth order differential equation and spectral properties of a 2nth order differential operator. These properties are established by the variational method based on the validity of some nth order differential inequality, where its weights are the coefficients of the equation and the operator. In turn, the inequality is characterized when the weights satisfy certain conditions that guarantee for the function in this inequality the existence of boundary values at infinity and at zero. AMS Subject Classification: Primary 34C10, 34K08; secondary 26D10