On the Multiplicity of Equilibrium Solutions to a Nonlinear Diffusion Equation on a Manifold Arising in Climatology

We analyze the sensitivity of a climatological model with respect to small changes in one of the distinguished parameters: the solar constant. We start by proving the stabilization of solutions of the evolution model when time tends to infinity. Later, we study the stationary problem and obtain uniqueness or a multiplicity of solutions for different values of the solar constant.