In this paper we provide a comparison principle for the weak solutions u(·,t),v(·,t)\documentclass[12pt]{minimal}
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\begin{document}$$u(\cdot ,t),v(\cdot ,t)$$\end{document} of two similar evolution p-Laplacian equations, both with source terms in a divergent and non-divergent form. Once we treat with signal solutions defined in all space Rn\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {R}^n$$\end{document}, for all t in a maximal existence interval [0,T∗)\documentclass[12pt]{minimal}
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\begin{document}$$[0,T_*)$$\end{document}, the arguments presented here differ from the ones used to prove the comparison principle in bounded domains. We suppose p≥n\documentclass[12pt]{minimal}
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\begin{document}$$p\ge n$$\end{document}, p>2\documentclass[12pt]{minimal}
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\begin{document}$$p>2$$\end{document} and also consider some additional natural assumptions. The initial conditions u(·,0)\documentclass[12pt]{minimal}
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\begin{document}$$u(\cdot ,0)$$\end{document} and v(·,0)\documentclass[12pt]{minimal}
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\begin{document}$$v(\cdot ,0)$$\end{document} are supposed to belong to the space L1(Rn)∩L∞(Rn)\documentclass[12pt]{minimal}
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\begin{document}$$L^{1}(\mathbb {R}^{n}) \cap L^{\infty }(\mathbb {R}^{n})$$\end{document}. An useful proposition to prove the comparison principle will be presented and the contraction of the L1\documentclass[12pt]{minimal}
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\begin{document}$$L^1$$\end{document} norm of u-v\documentclass[12pt]{minimal}
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\begin{document}$$u-v$$\end{document} for a particular case will be shown.
