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Math Help - Gateaux differential and Euler-Lagrange equation

  1. #1
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    Gateaux differential and Euler-Lagrange equation

    Hi! Can anyone help guide me through how to find the Gˆateaux differential and use
    it to derive the associated Euler–Lagrange equation for the following functional? Satisfying and boundary conditions also.

    Gateaux differential and Euler-Lagrange equation-mhf1.png

    Im really sorry, I was having so many problems with trying to create that in Latex, so I have attached a thumbnail showing the function needed, click it and theres a clear version of the function!

    Many thanks
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  2. #2
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    Re: Gateaux differential and Euler-Lagrange equation

    Sorry, I have no idea how to do your problem but I've been learning latex (very slowly) so I thought I would show you that.
    (I hope that you don't mind)

    S[y]=\int_1^2dx(3y'^2-2y^2),\;\;y=(1)\;\;y(2)=3.|
    Last edited by Melody2; December 10th 2013 at 04:58 AM.
    Thanks from sirellwood
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