American Institute of Mathematical Sciences

October  2010, 14(3): 1199-1210. doi: 10.3934/dcdsb.2010.14.1199

A class of doubly degenerate parabolic equations with periodic sources

 1 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China, China, China, China

Received  May 2009 Revised  March 2010 Published  July 2010

In this paper, we investigate a class of doubly degenerate parabolic equations with periodic sources subject 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 the eigenvalue problem for the $p$-Laplacian equation.
Citation: Jiebao Sun, Boying Wu, Jing Li, Dazhi Zhang. A class of doubly degenerate parabolic equations with periodic sources. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1199-1210. doi: 10.3934/dcdsb.2010.14.1199
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