# Eigenvalues of Linear operator

$L_2[0,pi]$ is the Hilbert space of complex square integrable functions on [0,pi] and D={f belongs to $L_{2}[0,pi]$ : f is twice continuously differentiable and f(0)=f(pi)=0)}.
let L :--> $L_2[0,pi]$ be the sturm-Liouville operator $Lf=-(e^xf')'$
show that $\geq0$ for all f in D. Further, show that all eigenvalues of L are positive.