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Math Help - Sturm-Liouville system

  1. #1
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    Sturm-Liouville system

    Dear all, how can I transfer the following general Sturm-Liouville equation

    [p(x)y']'+[q(x)+\lambda r(x)]y=0

    into the following special Sturm-Liouville equation

    y''+(\lambda +q(x))y=0?

    Thank you very much.
    Last edited by Ackbeet; July 28th 2011 at 02:12 AM.
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  2. #2
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    Re: Sturm-Liouville system

    There are some hints to the problem. It goes as follows.

    1. Take y=u(x)z, choose appropriate u(x), we can get \ddot z+A(x)z=0.

    2. Then take x=f(t) for some function f, we can see the result.

    However, I could not check the second hint.
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  3. #3
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    Re: Sturm-Liouville system

    I'll make one comment. If you do step 1. to eliminate z' then step 2. will put z' back into the ODE. I think what you what to do is steps 1. and 2. together.

    Also, I don't think you're going to get the same q(x).
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  4. #4
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    Re: Sturm-Liouville system

    Thank you very much for your help. And I've solved this problem in a very tedious way as you said. Good luck to you.
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