Abstract

This article develops an existence result for a general non-linear parabolic equation and related eigenvalue problem. The method of proof comprises a variational approach for establishing a concerning solution existence at each instant of time, related to a model discretized in time. The main difference concerning the previous version, is that we have made some improvements and corrections concerning a heuristic part of the previous proof, presenting now a formal rigourous result. In particular, as a novelty in this last version, we prove in details the minimizing sequences are uniformly bounded in an appropriate norm, independently of a natural parameter N which corresponds to the number of nodes for such a model discretized in time.