How to solve heterogeneous individual model steady state

Hello, professor. I have some questions when trying to solve the steady-state of a dual sector heterogeneous individual model. I set up a model similar to Rubio (2014), but I don’t know how to start when solving steady-state problems. Do you know any good hand solution?

poland.pdf (1.4 MB)

I am not totally sure, but I think that you may have a look at Matteo Iacoviello’s website. I think that you can find there some appendixes showing how he solves the steady-state of similar models

Thanks for your answers.I understand the measures.