On the sign-regularity of positive fourth-order differential operators

TL;DR

This paper establishes that the positivity of the Green function within the domain serves as a criterion for the sign-regularity of positive fourth-order differential operators with separated boundary conditions.

Contribution

It introduces a new criterion linking Green function positivity to sign-regularity for fourth-order differential operators.

Findings

Green function positivity implies sign-regularity.

Provides a criterion for analyzing fourth-order operators.

Applicable to operators with separated boundary conditions.

Abstract

It is shown that positivity in $(0,1)\times (0,1)$ of Green function of positively defined fourth-order ordinary differential operator (with separated boundary conditions) is a criterium of sign-regularity of this operator.