If we have
- An equation $E$ for which the conditions for the existence of a solution are satisfied but we can't prove the uniqueness of the solutions.
- A perturbed equation $E_p$ of $E$ which the existence and the uniqueness of solution are satisfied.
- The solutions $S_p$ of $E_p$ converge strongly to the solutions $S$ of $E$.
Question: Do (2) and (3) implies the uniqueness of solution in (1)?