A Dynamical Approach to the Perron-Frobenius Theory and Generalized Krein-Rutman Type Theorems

We present a new dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in the literature. As a result, we develop a complex version of the Perron-Frobenius theory and prove a variety of generalized Krein-Rutman type theorems for real operators. In particular, we establish some new Krein-Rutman type theorems for sectorial operators in a formalism that can be directly applied to elliptic operators, which allow us to reduce significantly the technical PDE arguments involved in the study of the principal eigenvalue problems of these operators.Comment: 40 page