國立清華大學 數學系

Abstract The main goal of this talk is discussing the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger, as previous steps towards the theorem of characterization of the strong maximum principle of López-Gómez, Molina-Meyer and Amann, which generalizes, very substantially, a popular result of Berestycki, Nirenberg and Varadhan. Then, it will be shown how such a characterization allows us to algebrize the analysis of the search for positive solutions in a generalized class of diffusive logistic equations.