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 , 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.
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| Imre Voros |
Department of Applied Analysis
Eotvos Lorand University Budapest, Hungary
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