Does this PDE admit steady state solutions?

[mbp]

Hello to everyone. I am new with this forum and I am asking help with PDE.

I have a linear PDE:
L f(x,y,t) = 0
where L is a second order linear operator depending on x, y, their partial derivatives, and t, but not on derivatives with respect to t. The question is: does this PDE in general admit steady state (time independent) solutions f(x,y)?

Thanks in advance.

 

[hunt_mat]

Set all derivative terms w.r.t. t equal to zero and see if you can solve it.