Periodic solutions for degenerate diffusion equations
Noriko Mizoguchi · Indiana University Mathematics Journal · 1995
In this paper, we are concerned with the existence of nonnegative periodic solutions ofwith the Dirichlet boundary condition, where m > 1, Ω is a smoothly bounded domain in R N and h is a given positive periodic function on R. The forcing term in this paper satisfiesfor example, f (u) = u p with p ≥ m and h > λ 1 .We adapt the Leray-Schauder degree theory in the proof.To do that, we need an a priori estimate for solutions in L ∞ .Inequalities of Harnack type and the blow up (or scaling) argument play crucial parts.