Oscillation theorems for the Sturm–Liouville problems with potential-distributions / A. A. Shkalikov, J. Ben Amara. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 3. P.
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 132-137].
The Sturm–Liouville problem
\begin{matrix}
-y"+q(x)y=\lambda y,\\
y(0)=y(1)=0
\end{matrix}
is considered with a singular potential q(x) representing
the derivative of a real function from the space L_2[0,1]
in the distributional sense.
Two approaches are developed for the study of oscillation
properties of eigenfunctions of this problem.
The first approach is based on generalization of methods of the
Sturm theory. The second one is based on development of
variational principles.