Research Article Periodic Solutions of Evolution m-Laplacian Equations witha Nonlinear Convection Term

where Ω RN (N 1) is a bounded domain with smooth boundary ∂Ω, ω > 0, m > 1, and b(u) is a nonlinear vector field such that b(u) k u β, with some k > 0, 0 β m 1. f (t) and h(x, t) are ω-periodic (in t) functions. Equation (1.1) is a class of degenerate parabolic equations and appears to be relevant in the theory of non-Newtonian fluids perturbed by nonlinear terms and forced by rather irregular period in time excitations, see [1, 2] for instance. The term b(u) u describes an effect of convection with a velocity field b(u). In the last two decades, periodic parabolic equations have been the subject of extensive study (see [3–11]). In Particular, Nakao [7] considered the following equation: