Can you give a nonconstant function to show difference between The Weak Maximum Principle and The Strong Maximum Principle

Question

We know that the Weak Maximum Principle and Strong Maximum Principle in every PDE book,such as Theorem 3.1 and Theorem 3.5 in David Dilbarg's book. But I never see a author give a nonconstant function as a example can attain it's interior maximum (also on boundary) for the weak principle maximum. Is the example so difficult that they don't provide it ? or the weak maximum principle is the same as the strong maximum principle. In brief, I want an elliptic operator that satisfies the weak maximum principle but not the strong one.