I would really appreciate if someone could just write down for me one example of a second order, or higher, differential equation for which it is known that there are no smooth solutions; and it's fine if it's a partial differential equation.
At first I thought it would be easy to either come up with an example or else find one by searching google/wiki/arxiv; but now I am not so sure.
I have a thing for non-smooth functions, and it just bothers me that I don't even know a single example of this type of differential equation. Thanks!