Some new aspects of perturbation theory of positive solutions of second-order linear elliptic equations

TL;DR

This paper explores new theoretical insights into how positive solutions of second-order linear elliptic equations behave under perturbations, focusing on Green functions and comparison principles.

Contribution

It introduces novel results on the equivalence of Green functions and extends Liouville comparison principles to nonsymmetric operators.

Findings

Established conditions for Green function equivalence

Extended Liouville comparison principles

Analyzed perturbation effects on positive solutions

Abstract

We present some new results concerning perturbation theory for positive solutions of second-order linear elliptic operators, including further study of the equivalence of positive minimal Green functions and the validity of a Liouville comparison principle for nonsymmetric operators.