Estimate of the validity interval for the Antimaximum Principle and application to a non-cooperative system

Abstract

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.