THE STRUCTURE OF THE PRINCIPAL COMPONENT FOR SEMILINEAR DIFFUSION-EQUATIONS FROM ENERGY-BALANCE CLIMATE MODELS

This paper deals with a class of parameter dependent semilinear diffusion problems from climate modeling on a 2-dimensional oriented Riemannian manifold or on [-1,1] involving a Legendre type diffusion operator. A qualitative framework is described, where the principal component of the set of stationary solutions forms an S-shaped Jordan curve. Our approach is based on results due to Amann [1,2] and Crandall, Rabinowitz [6] with the implicit function theorem and continuation arguments as main tools.