Signed networks are a crucial tool when modeling friend and foe relationships. In contrast to classical undirected, weighted graphs, the edge weights for signed graphs are positive and negative. Crucial network properties are often derived from the study of the associated graph Laplacians. We here study several different signed network Laplacians with a focus on the task of classifying the nodes of the graph. We here extend a recently introduced technique based on a partial differential equation defined on the signed network, namely the Allen-Cahn-equation, to classify the nodes into two or more classes. We illustrate the performance of this approach on several real-world networks.