Principal eigenvalue and maximum principle for cooperative periodic-parabolic systems

Abstract

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.