Jacqueline Fleckinger
Jesús Hernández
François de Thélin

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

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 69, 19 - 32 (2014/15)

MSC: 35J57   Boundary value problems for second-order elliptic systems
  35B50   Maximum principles
  35B09   Positive solutions

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.

Keywords:   Maximum Principle, Antimaximum Principle, Elliptic Equations and Sys- tems, Non cooperative systems, Principal Eigenvalue.

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