Afternoon all, I was hoping someone might be able to give me some pointers on where to go with this problem.
"3. (a) Use eigenfunction expansion to nd the bounded solution of
on -1 =< x =< 1 [Hint: write the equation in self-adjoint form to determine which
expansion functions to use.]
(b) What can you say about the solution of
with u again bounded on [-1,1]?"
Probably the easiest way is for me to outline what I've done, and then (hopefully) someone can either show me where I've gone wrong, or give me some pointers on where to go next.
For 3) a) I first converted the function to self adjoint form through the process:
Using an integrating factor of
To give
Which at first looked like it had a simmilar form to Legendre or Chebyshev, but now I'm not sure. It's defiently a singular Sterm-Liouville system though, rather than a periodic or Regular SL system, as they go to infinity at the end points, which I'm pretty sure satisfies the singular SL system conditions.
But it's at this point I got pretty damn stuck.
I think the next step is to go and do
[img]http://latex.codecogs.com/gif.latex?L(u)+\lambda\rho*u=0[/img]
Which actually is starting to look like it's taking the form of a Hermite DE, but I'm not really sure, especially since hermites exist on
So....any help possible?
Much obliged.