Time Periodic Solutions for a Diffusive Energy Balance Model in Climatology

We prove the existence of a periodic solution to the problem utyDpuqRe x, u.gmQ x, t.b u. in M=R, assumed pG2, M a compact connected and oriented bidimensional Riemannian manifold without boundary, b u. a bounded maximal monotone graph the coalbedo., Q x, t.a time periodic function the incoming solar radiation flux.and Re a time independent strictly increasing function of the surface temperature u the Earth emitted energy..