  Generalized models provide a framework for the study of evolution equations
without specifying all functional forms. The generalized formulation of
problems has been shown to facilitate the analytical investigation of local
dynamics and has been used successfully to answer applied questions. Yet their
potential to facilitate analytical computations has not been realized in the
mathematical literature. In the present paper we introduce the method of
generalized modeling in mathematical terms, supporting the key steps of the
procedure by rigorous proofs. Further, we point out open questions that are in
the scope of present mathematical research and, if answered could greatly
increase the predictive power of generalized models.
