Self-similar functions in $L_2[0,1]$ and Sturm--Liouville Problem with singular indefinite weight

In the paper the Sturm-Liouville problem $-y^{\mathrm{\prime }\mathrm{\prime }}-\rho y=0$, $y(0)=y(1)=0$ is studied. $\rho$ is a generalized derivative of function $P\in L_2[0,1]$. For self-similar $P$ asymptotic formulas for eigenvalues are obtained.