Weighted Second-Order Differential Inequality on Set of Compactly Supported Functions and Its Applications

Abstract

In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality of independent interest.

Keywords

• weighted inequality
• fourth-order differential operator
• oscillation
• non-oscillation
• spectrum discreteness
• spectrum positive definiteness