  For the Ekpyrotic universe, the entropic mechanisms with minimal couplings,
which have been used to generate nearly scale invariant primordial
perturbations, was proved to be unstable. To overcome this difficulty, some
non-minimal coupling entropic models were proposed. In this paper we extend
these studies to the cases where all the scalar fields have non-standard
kinetic terms. We first prove that in these general cases, without non-minimal
couplings the entropic models are still unstable. The condition for the
stability conflicts with the requirement for achieving scale invariant
perturbations. Then we study the non-minimal coupling models and show that at
least for some simple cases these models are stable and able to generate the
primordial perturbations consistent with current observations.
