Strong Positivity in C(Omega) for Cooperative Elliptic Systems

摘要

A maximum for cooperative systems of elliptic equations is presented. Recentlythe problem has been revisited by several authors. Nagel uses semigroup theory for operator matrices and finds as an application a positivity result for the elliptic system. A direct proof is presented by using an extension of the Krein-Rutman Theorem. The underlying space is (C(omega))(exp k). In this approach it is sufficient to have operators with continuous coefficients and little regularity of the boundary of the domain. The existence of a unique first eigenfunction is shown.