Geodesic
Stability properties of non-negative solutions of semilinear symmetric cooperative systems
Electronic journal of differential equations, Tome 2004 (2004)
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).
Classification : 35K57, 35B35
Keywords: cooperative semilinear system, positive stationary solutions 
@article{EJDE_2004__2004__a121,
     author = {Voros,  Imre},
     title = {Stability properties of non-negative solutions of semilinear symmetric cooperative systems},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1073.35108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a121/}
}
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%A Voros,  Imre
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%J Electronic journal of differential equations
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Voros,  Imre. Stability properties of non-negative solutions of semilinear symmetric cooperative systems. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a121/