Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 105, pp. 1-6.

Title: Stability properties of non-negative solutions of 
  semilinear symmetric cooperative systems

Author: Imre Voros (Eotvos Lorand Univ., Budapest, Hungary)
 
Abstract: 
 We investigate the stability of non-negative stationary solutions of
 symmetric cooperative semilinear systems with some convex (resp.
 concave) nonlinearity condition,  namely all second-order partial
 derivatives of each coordinate being non-negative (resp. non-positive).
 In these cases, we will show following [8], extending its results,
 that this along with some sign condition on the non-linearity at the
 origin yields instability (resp. stability).
 
Submitted May 25, 2004. Published September 8, 2004.
Math Subject Classifications: 35K57, 35B35.
Key Words: Cooperative semilinear system; positive stationary solutions.