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Unfortunately, there is no literature on this that I am aware of. The thing is that after dropping all time subscripts, you simply have to solve a system of nonlinear equations. There are some tricks you get to know with some practice, but I am not sure anyone has ever really written them down.
What do you mean with "Theory"? You are solving a nonlinear equation system. Depending on how the equations look like, theory might tell you whether there exists a unique steady state. For example, in the Solow model, the theory tells us there are two steady states: the regular one and the trivial one at 0.