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Non-trivial non-negative periodic solutions of a system of doubly degenerate parabolic equations with nonlocal terms

2011
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Discrete and Continuous Dynamical Systems. Series A
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The aim of the paper is to provide conditions ensuring the existence of non-trivial non-negative periodic solutions to a system of doubly degenerate parabolic equations containing delayed nonlocal terms and satisfying Dirichlet boundary conditions. The employed approach is based on the theory of the Leray-Schauder topological degree theory, thus a crucial purpose of the paper is to obtain a priori bounds in a convenient functional space, here L 2 (Q T ), on the solutions of certain homotopies.

doi:10.3934/dcds.2011.31.35
fatcat:eoa7fuzxgzcotauonnokullije