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If we have

  1. 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.
  2. A perturbed equation $E_p$ of $E$ which the existence and the uniqueness of solution are satisfied.
  3. 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)?

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    What kind of equation? Algebraic? Differential? Why is there a tag of [probability]?2011-01-30
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    Exemple Let u'+Au =f .................. (E) u'+Au+pBu=f ............... (Ep) (E) and (Ep) are two PDE or ODE, A and B are two differential operators, p is a parameter. When p goes to zero, we get E and the solution of (Ep) converges to the solution of (E).2011-01-30
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    Dear Hafid: additional information should be posted as a comment or edited into the question statement.2011-01-30

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