- #1
libelec
- 176
- 0
For a Sturm-Liouville problem, as in:
[tex]\frac{d}{{dx}}\left[ {r(x)\frac{{dy}}{{dx}}} \right] + [\lambda p(x) + q(x)]y = 0[/tex]
I've read in several books that one assumes that p, q and r are continuous, real-valued and bounded in the interval I, r' is continuous, and p>0.
But I've never seen or understood the reason why we make this assumption. What's the difference? Can't p be complex-valued? Why can't q be unbounded?
[tex]\frac{d}{{dx}}\left[ {r(x)\frac{{dy}}{{dx}}} \right] + [\lambda p(x) + q(x)]y = 0[/tex]
I've read in several books that one assumes that p, q and r are continuous, real-valued and bounded in the interval I, r' is continuous, and p>0.
But I've never seen or understood the reason why we make this assumption. What's the difference? Can't p be complex-valued? Why can't q be unbounded?