- #1
meteorologist1
- 100
- 0
I'm stuck on the following eigenvalue problem:
[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!
[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!