Positivity for a noncooperative system of elliptic equations in $\mathbb{R}^N$

Abstract

Elliptic systems with noncooperative coupling in general do not preserve positivity. Here it is shown that some systems of elliptic equations on $ \mathbb{R}^N$ with small noncooperative coupling still have a restricted uniform positivity preserving property. The proofs rely on optimal estimates for the Newtonian potential with weights and on corresponding $3G$-type theorems.