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# Need help-eigenvalue problem Watch

1. Hey!!!

Knowing that:
"The eigenvalue problem is a Sturm-Liouville problem when it satisfies the boundary conditions:
,where is the wronskian."

I have to show that the eigenvalue problem , with boundary conditions is not a Sturm -Liouville problem.

This is what I've done so far:

Let solutions of the eigenvalue problem , then:
and .

How can I continue? How can I show that this is not equal to 0?
2. (Original post by mathmari)
Hey!!!

How can I continue? How can I show that this is not equal to 0?
Could you not find and show it that way? Seems like cheating, but I don't see why you shouldn't do it.
3. (Original post by Smaug123)
Could you not find and show it that way? Seems like cheating, but I don't see why you shouldn't do it.
I have found the eigenfunctions of the eigenvalue problem.They are .If we suppose that and are solutions of the eigenvalue problem,do I have to take two different at the eigenfunction to find and ? I got stuck right now..
4. (Original post by mathmari)
I have found the eigenfunctions of the eigenvalue problem.They are .If we suppose that and are solutions of the eigenvalue problem,do I have to take two different at the eigenfunction to find and ? I got stuck right now..
Hmm, now I'm confused. Because it's not a Sturm-Liouville problem, we aren't guaranteed to have a complete set of eigenfunctions, so we can't proceed by expressing u and v as a sum of eigenfunctions. I'm stumped, I'm afraid
5. (Original post by Smaug123)
Hmm, now I'm confused. Because it's not a Sturm-Liouville problem, we aren't guaranteed to have a complete set of eigenfunctions, so we can't proceed by expressing u and v as a sum of eigenfunctions. I'm stumped, I'm afraid
Oh ok... How did you mean it that I could find and ?
6. (Original post by mathmari)
Oh ok... How did you mean it that I could find and ?
In hindsight, I was assuming that any u and v could be expanded in terms of eigenfunctions. That's true for Sturm-Liouville problems, but not necessarily for non-SL ones.
7. (Original post by Smaug123)
In hindsight, I was assuming that any u and v could be expanded in terms of eigenfunctions. That's true for Sturm-Liouville problems, but not necessarily for non-SL ones.
Aha! Ok! Do you have any other idea what I could do?

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