On Time Periodic Solutions of the Dirichlet Problem for Degenerate Parabolic Equations of Nondivergence Type

In this paper, we are concerned with the existence of periodic solutions of a quasilinear parabolic equation utsug Duquqf. in V=R with the Dirichlet boundary condition, where V is a smoothly bounded domain in RN and f is a given function periodic in time defined on V=R. Our results depend on the first eigenvalue l1 of yD in V with the Dirichlet boundary condition. If l1)1, then there exists a unique positive periodic solution for a positive f g gR.. In the case of l1-1, we construct a nonnegative periodic solution for a negative f 1Fg -3..