## Advances in Differential Equations

### 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.

#### Article information

Source
Adv. Differential Equations, Volume 4, Number 1 (1999), 115-136.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366291800

Mathematical Reviews number (MathSciNet)
MR1667285

Zentralblatt MATH identifier
0947.35050

#### Citation

Stavrakakis, Nikos; Sweers, Guido. Positivity for a noncooperative system of elliptic equations in $\mathbb{R}^N$. Adv. Differential Equations 4 (1999), no. 1, 115--136. https://projecteuclid.org/euclid.ade/1366291800