Periodic Solutions of Evolutionp-Laplacian Equations with Nonlinear Sources

In this paper, we are concerned with the time periodic solutions to the evolutionp-Laplacian equations of the form[formula]and[formula]with the Dirichlet boundary value condition, wherep≥2, ω0,Ω is a bounded convex domain inR^Nwith smooth boundary ∂Ω,m(x,t) is continuous onΩ×R, periodic intwith period ω and positive in Ω×R. The existence of nontrivial nonnegative periodic solutions is established provided thatN1 andp-1<α<p-1+p/N.