On time periodic solutions of the Dirichlet problem for degenerate parabolic equations of nondivergence type

Abstract In this paper, we are concerned with the existence of periodic solutions of a quasilinear parabolic equation[formula]with the Dirichlet boundary condition, where Ω is a smoothly bounded domain inRNandfis a given function periodic in time defined on[formula]. Our results depend on the first eigenvalue λ1of −Δ in Ω with the Dirichlet boundary condition. If λ1>1, then there exists a unique positive periodic solution for a positivef(γ∈R). In the case of λ1