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Math Help - PDE - show that the principle eigenfunction is not sign changing

  1. #1
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    PDE - show that the principle eigenfunction is not sign changing

    Studying for a test

    a) show that the principle eigenfuntion is not sign changing
    b) show all the other eigenfunctions are sign changing.

    i'm not sure what this mean or what i meant by "princple"

    can anone point me in the right direction?
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  2. #2
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    The "principle eigenvalue" is the one that is largest in absolute value.
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  3. #3
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    i have in my notes that all of the eigenvalues are positive
    wouldn't all of the eigenfunctions also be positive?

    my professor mentioned something in class about the fact that

    Int(u_1*u_m*rho dx)=0

    >>> u_1>0, rho>0

    >>> u_m must be sign changing


    i think that what he said is pretty much all of it, but i really don't know what it means and i don't have anyone around that is in pde with me to ask... i have a test on friday... HELP

    i'm not sure why these questions are relevant
    i am under the impression that if something is sign changing it will cancel to zero when you comupet the integral, but then the whole integral would be zero....
    and i always get confused when i get a lot of zeros, because it normally means i have made a mistake...
    Last edited by mlemilys; April 22nd 2009 at 12:51 PM.
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