I have an equation in the model block of dynare but because of the non-linearity there is no explicit solution for the variable. Basically, I have the same variable in the both side of the equation, which the variable I need to have a solution.

I am not sure if that makes sense, but Can I write an m. file for this equation using fzero matlab command which gives numeric values for the variable and include this m file into the model block?

I am not sure I understand your problem here. It is perfectly legal to have the same variable on both sides of an equation. When you will simulate the model, you will obtain a solution for the variable (obviously this solution will depend on how you approximate the model).

If you have a matlab function to compute a variable (or a parameter) you can use an external function in the model block (this is described in the reference manual here.

Hello Dr Pfeifer
When I run the model it can not compute the steay state, there are big residuals for 3 equations, for others zero. The biggest non zero residual is related to the L, I still can not see What the problem this equation might have.