I have the following question for you, if you can help me.

I tried to solve a dsge model, but I have the following problem. Even though I have written steady-state relations analytically, when I run the code, there is no steady-state.

If you truly have computed the steady state correctly, then your initval block should show 0 residuals as the steady state must solve the static model equations. As that is not the case, one of the two is wrong.