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Genericity of Uniquness of a Solution to a System with Non-Linear Equations

  1. Dec 11, 2008 #1
    Dear All,

    I have maybe quite a naive question:

    Does there exist a result that a generic system of non-linear equations have a unique solution??? (defined from R^n to R)

    Similarily as it exists a result that a generic square matrix could be inverted?

    Waiting impatiently for news! Thanks!

    Le Cactus
     
  2. jcsd
  3. Dec 12, 2008 #2
    There are lots and lots and lots of nonlinear PDEs that can't be solved uniquely. However, there are classes of PDEs we understand well that have unique solutions in given function spaces. Do you have a particular PDE in mind?
     
  4. Dec 12, 2008 #3
    Thank you for answering!
    Actually I have a much simplier structure on the system than PDE. It is just a system of K arbitrary polynoms (of finite order)...
    I am currently trying to see if the transversality theorem does not apply (or if it applies under which conditions on a system), but for the moment all the things remain to be murky :confused:
    May be there are existent results...?

    Thanks!
     
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