I'm stuck on the following eigenvalue problem:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] u^{iv} + \lambda u = 0, 0 < x < \pi [/tex]

with the boundary conditions u = u'' = 0 at x = 0 and pi.

("iv" means fourth derivative)

I look at the characteristic polynomial for lambda > 0 and < 0 and I get fourth roots for each of them. In the case for lambda < 0, I get 2 real roots and 2 complex roots. In the case lambda > 0, I get 4 complex roots. But what I need to show is that all eigenvalues are real, and what the signs of the eigenvalues are, and what the eigenvalues are.

Please help! Thanks!

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# Fourth-order eigenvalue problem

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