How to stationarize an endogenous discount factor

Hi Suppose that I have a model in which TFP is increasing, call the TFP: At,
and Consumption Ct is increasing at the same order with TFP, thus Ct/At is stationary

How do I stationarize an endogenous discount factor

Some literature uses this kind of endogenous discount factor in their utilities, but I never found any way to stationarize v(Ct,Lt).

The easiest way is to assume that this functional form for the endogenous discount factor applies to the stationarized model, i.e. the C_t is the detrended one. Otherwise, the functional form you provide is inconsistent with a balanced growth path.