Consider the Sturm-Liouville Problem u'' + [c - q(x)]u = 0 with endpoint conditions a1u(a) + a2u'(a) = 0, b1u(b) + b2u'(b) = 0. Show that all eigenvalues of this S-L system (values of c) are positive if q(x) > 0, a1*a2 < 0, b1*b2 > 0.
I tried writing the problem using a Prufer substitution, but I'm not any closer to getting a contradiction assuming c < 0. Any ideas?
Thanks in advance.