Why does this blow up?

rsq_a

I'm looking at the BVP:

[tex]y'' + ay' + e^{ax}y = 1[/tex],

with y(0) = 0 and y(10) = 0.

The numerical solution blows up at certain values of [tex]a[/tex]. For example, a near 0.089 and a near 0.2302. Why does this happen and how do I predict it?

rsq_a

Erm. I found the problem. Near those values of 'a', there exists a zero eigenvalue of the linear operator. I guess that means that,

[tex]y'' + ay' + e^{ax}y = 0\cdot u^* = 1[/tex],

is a possible solution, and thus the eigenfunction [tex]u^* \to \infty[/tex] will cause the blowup.

Is this correct? It's been a while since I've done Sturm-Liouville stuff.

jacophile

What is x?

rsq_a

[tex]y=y(x)[/tex]