Variational Structure of Energy-Balance Climate Models with Heterogeneous Insolation

We analyse stationary Sellers-type energy-balance climate models with heterogeneous insolation $Q_\varepsilon = Q_*+\varepsilon Q_1$, both on the interval $(-1,1)$ with degenerate diffusion $κ(x)=1-x^2$ and on $\mathbb{S}^2$ with uniformly elliptic diffusion. Assuming that the homogeneous model corr