Principal eigenvalue and maximum principle for cooperative periodic–parabolic systems

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This paper classifies the set of supersolutions of a general class of periodic–parabolic problems in the presence of a positive supersolution. From this result we characterize the positivity of the underlying resolvent operator through the positivity of the associated principal eigenvalue and the existence of a positive strict supersolution. Lastly, this (scalar) characterization is used to characterize the strong maximum principle for a class of periodic–parabolic systems of cooperative type under arbitrary boundary conditions of mixed type.