## spectral decomposition, Sturm–Liouville

consider A : L2[0,1] --> L2[0,1] : Af(s) = integral (from 0 to 1) max{s,t}*f(t)dt
I've shown that the operator is compact and self-adjoint. Looking for the euginevalues.
Af(s) = cf(s) = integral (from 0 to 1) max{s,t}*f(t)dt
then c*df/ds = integral (from 0 to s) f(t)dt
and c*d^2f/ds^2 = f(s)
obviously df(0)/ds = 0.
How can I get another initial condition?