On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients

In the paper we consider singular spectral Sturm–Liouville problem $-(p{y}^{\mathrm{\prime }}{)}^{\mathrm{\prime }}+(q-\lambda r)y=0$, $(U-1)y^{\vee }+i(U+1)y^{\wedge }=0$, where function $p\in L_{\mathrm{\infty }}[0,1]$ is uniformly positive, generalized functions $q,r\in W_2^{-1}[0,1]$arereal-valuedandunitarymatrix$U\in\mathbb C^{2\times 2}$ is diagonal. The main goal is to prove that well-known (for smooth case) facts about number and distribution of zeros of eigenfunctions hold in general case.