Time periodic solutions of a class of degenerate parabolic equations

This paper is devoted to the time periodic solutions to the degenerate parabolic equations of the form ∂u/∂t=Δu^m+u^p(a(x,t)-b(x,t)u) in Ω×R under the Dirichlet boundary value condition, where m>1, p≥0, Ω⊂R^N is a bounded domain with smooth boundary ∂Ω and a,6 are positive, smooth functions which are periodic in t with period ω>0. The existence of nontrivial nonnegative solutions is established provided that 0≤p<m. The existence is also proved in the case p=m but with an additional assumption min/Q a(x,t)>λ₁, where λ₁ is the first eigenvalue of the operator -Δ under the homogeneous Dirichlet boundary condition.