The maximum principle for cooperative weakly coupled elliptic systems and some applications

Abstract

In this work we obtain some characterizations of the maximum principle for weakly coupled elliptic cooperative systems. Roughly speaking, it is shown that a cooperative system behaves as one single equation. This fact is used to analyze the existence and uniqueness of positive principal eigenvalues for some boundary value problems associated with the system. The theory developed here provides us with a systematic analysis procedure sharpening most of the results in the references. This establishment of connections and relationships between the different problems treated separately in the literature is our main goal. © 1994, Khayyam Publishing.