Consider the boundary value problem:

y'' + q(x)y = lambda * y

y'(0) = y'(2) = 0

x in [0,2]

Show that if q(x) is continuous and q_- <= q(x) <= q_+ for x in [0,2], then this BVP has a solution for some lambda in [ (q_-) - 1 , (q_+) - 1]

I think the BVP is a Sturm Liouville problem, but in class we've only dealt with the case of q(x) = constant. So, I'm not sure where to go with this one at all. Any help would be greatly appreciated.