|MSC:||35J57||Boundary value problems for second-order elliptic systems|
We are concerned with the sign of the solutions of non-cooperative systems
when the parameter varies near a Principal eigenvalue of the system. With this aim we give
precise estimates of the validity interval for the Antimaximum Principle for an equation and
an example. We apply these results to a non-cooperative system. Finally a counterexample
shows that our hypotheses are necessary. The Maximum Principle remains true only for a
restricted positive cone.