Stability properties of non-negative solutions of semilinear symmetric cooperative systems
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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).
CitationVoros, I. (2004). Stability properties of non-negative solutions of semilinear symmetric cooperative systems. Electronic Journal of Differential Equations, 2004(105), pp. 1-6.
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