Advances in Differential Equations

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

Nikos Stavrakakis and Guido Sweers

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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

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

First available in Project Euclid: 18 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B50: Maximum principles 35J45, 31B30: Biharmonic and polyharmonic equations and functions


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.

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