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

Abstract: We present a 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 some generalized Krein-Rutman type theorems.