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# A class of doubly degenerate parabolic equations with periodic sources

• 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.
Mathematics Subject Classification: 35K57, 35K65, 35B10.

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