On Volterra three-point problems for the Sturm-Liouville operator related to potential symmetry (Q1731502)

The authors consider the three-point problem \[ \begin{aligned} & -y^{\prime\prime}(x)+q(x)y(x)-\lambda y(x)=0,\ 0< x < \pi, \\ & y(0)-k_1 y(\pi)+k_2(1-k_1) y(\tfrac{\pi}{2})=0, \\ & y^{\prime}(0)+k_1 y^{\prime}(\pi)-k_2(1+k_1) y^{\prime}(\tfrac{\pi}{2})=0, \end{aligned} \] where $k_1,k_2\neq0,\infty$ and $q(x)$ is a complex-valued integrable function on $(0,\pi)$. They prove that this problem is Volterra when $q(x)=q(\pi-x)$, $x\in\left[ 0,\frac{\pi}{2}\right]$; $q(x)=q(\frac{\pi}{2}-x)$, $x\in\left[ 0,\frac{\pi}{4}\right]$ and $k_1,k_2\neq\pm1$.