On positive solutions of second-order elliptic equations, stability results, and classification (Q1826026)

The author studies the structure of the set \(C_ P(\Omega)\) of all positive solutions of the equation \(Pu=0\) in \(\Omega\), where P is a second-order uniformly elliptic operator defined in an (unbounded) domain \(\Omega \subset {\mathbb{R}}^ n\). By showing suitable estimates for the corresponding Green function he is able to prove various perturbation results for the set \(C_ P(\Omega)\). He considers the perturbations \(P'\) of the operator P, where either the coefficients of \(P'\) differ from the coefficients of P only in a bounded set or \(P'=P+tW,\) where W is a bounded Hölder continuous function.