# Discard trivial solutions to pde

I am interested in the following: suppose one has proved theoretically the existence of solution $$u = u (x_1,...,x_n)$$ of some pde. I wonder how can be shown that the obtained solution $$u$$ is not trivial, meaning that is not constant or depends on all variables $$x_1,...,x_n$$. Which are the main techniques to prove that kind of things?