Geodesic
Stability properties of non-negative solutions of semilinear symmetric cooperative systems
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Voros, Imre},
     title = {Stability properties of non-negative solutions of semilinear symmetric cooperative systems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a21/}
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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__a21/