A class of doubly degenerate parabolic equations with periodic sources
Jiebao Sun, Boying Wu, Jing Li, Dazhi Zhang · Discrete and Continuous Dynamical Systems - B · 2010
In this paper, we investigate a class of doubly degenerate parabolic equations with periodic sourcessubject to homogeneous Dirichlet boundary conditions.By means of the theory of Leray-Schauder degree,we establish the existence of non-trivial nonnegative periodic solutions.The key step is how to establish the uniform bound estimate of approximate solutions,for this purpose we will make use of Moser iteration and some results of theeigenvalue problem for the $p$-Laplacian equation.