### Periodic solutions of non-autonomous second order systems with $p$-Laplacian.

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De Pablo et al. [Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 513-530] considered a nonlinear boundary value problem for a porous medium equation with a convection term, and they classified exponents of nonlinearities which lead either to the global-in-time existence of solutions or to a blow-up of solutions. In their analysis they left open the case of a certain critical range of exponents. The purpose of this note is to fill this gap.

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